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# Personal Finance

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## Personal FinanceDocument Transcript

• 12 Essentials of Mathematics 12 Chapter Project In the project for this chapter, you will imagine that you are buying a home. You will choose the type of home you would like—a house, a condominium, a townhouse, or an alternative type of housing—and research the total cost of buying this home. You will then investigate if and when such a home might be affordable for you. As you complete the project activities, you will add the following items to your project file: 1. A description of the type of home you would like to purchase and information on three financial institutions that offer mortgages. 2. Calculations showing monthly, accelerated bi-weekly, and accelerated weekly mortgage payment options. 3. A calculation of the gross debt service ratio to see whether your purchase is affordable. 4. Calculations of the annual property insurance premiums from three companies. 5. Calculations showing the additional one-time costs associated with buying the home. Researching the costs involved in buying a home, such as this house in Winnipeg, is the project for this chapter.
• 14 Essentials of Mathematics 12 Table 1 Ten-Year Term Life Insurance Annual Premium for Term Plus Male Non-Smoker Female Non-Smoker Male Smoker Female Smoker Issue Rate per \$1,000 Issue Rate per \$1,000 Issue Rate per \$1,000 Issue Rate per \$1,000 \$100,000 – \$250,000 – \$500,000 – \$100,000 – \$250,000 – \$500,000 – \$100,000 – \$250,000 – \$500,000 – \$100,000 – \$250,000 – \$500,000 – Age \$249,999 \$499,999 \$3,000,000 \$249,999 \$499,999 \$3,000,000 \$249,999 \$499,999 \$3,000,000 \$249,999 \$499,999 \$3,000,000 20 0.85 0.81 0.77 0.80 0.76 0.73 1.43 1.36 1.30 1.32 1.25 1.20 21 0.85 0.81 0.77 0.80 0.76 0.73 1.43 1.36 1.30 1.32 1.25 1.20 22 0.85 0.81 0.77 0.80 0.76 0.73 1.43 1.36 1.30 1.32 1.25 1.20 23 0.85 0.81 0.77 0.80 0.76 0.73 1.43 1.36 1.30 1.32 1.25 1.20 24 0.85 0.81 0.77 0.80 0.76 0.73 1.43 1.36 1.30 1.32 1.25 1.20 25 0.85 0.81 0.77 0.80 0.76 0.73 1.43 1.36 1.30 1.32 1.25 1.20 26 0.86 0.82 0.78 0.80 0.76 0.73 1.47 1.40 1.34 1.33 1.27 1.21 27 0.87 0.83 0.79 0.80 0.76 0.73 1.52 1.44 1.39 1.34 1.28 1.22 28 0.88 0.84 0.80 0.80 0.76 0.73 1.56 1.49 1.42 1.35 1.29 1.23 29 0.89 0.85 0.81 0.80 0.76 0.73 1.61 1.53 1.46 1.36 1.30 1.24 30 0.90 0.86 0.82 0.80 0.76 0.73 1.65 1.57 1.51 1.38 1.31 1.25 31 0.96 0.91 0.87 0.86 0.82 0.78 1.78 1.69 1.62 1.47 1.40 1.34 32 1.02 0.97 0.93 0.92 0.87 0.84 1.91 1.82 1.74 1.57 1.50 1.43 33 1.08 1.03 0.98 0.98 0.93 0.89 2.05 1.95 1.86 1.67 1.58 1.52 34 1.14 1.08 1.04 1.04 0.99 0.95 2.18 2.07 1.98 1.77 1.68 1.62 35 1.20 1.14 1.09 1.10 1.05 1.00 2.31 2.20 2.10 1.87 1.78 1.71 36 1.34 1.27 1.22 1.17 1.11 1.06 2.60 2.46 2.37 2.02 1.93 1.84 37 1.48 1.41 1.35 1.24 1.18 1.13 2.88 2.74 2.62 2.18 2.07 1.98 38 1.62 1.54 1.47 1.31 1.24 1.19 3.17 3.01 2.88 2.33 2.21 2.12 39 1.76 1.67 1.60 1.38 1.31 1.26 3.45 3.28 3.15 2.49 2.37 2.27 40 1.90 1.81 1.73 1.45 1.38 1.32 3.74 3.55 3.40 2.64 2.51 2.40 41 2.06 1.96 1.87 1.56 1.48 1.42 4.22 4.02 3.84 2.90 2.76 2.64 42 2.22 2.11 2.02 1.67 1.59 1.52 4.71 4.48 4.28 3.17 3.01 2.88 43 2.38 2.26 2.17 1.78 1.69 1.62 5.19 4.93 4.73 3.43 3.26 3.12 44 2.54 2.41 2.31 1.89 1.80 1.72 5.68 5.39 5.17 3.70 3.51 3.37 45 2.70 2.57 2.46 2.00 1.90 1.82 6.16 5.85 5.61 3.96 3.76 3.61 46 3.03 2.88 2.76 2.23 2.12 2.03 6.60 6.27 6.01 4.49 4.27 4.08 47 3.36 3.19 3.06 2.46 2.34 2.24 7.04 6.69 6.40 5.02 4.76 4.57 48 3.69 3.51 3.36 2.69 2.56 2.45 7.48 7.11 6.81 5.54 5.27 5.05 49 4.02 3.82 3.66 2.92 2.77 2.66 7.92 7.52 7.21 6.07 5.76 5.52 50 4.35 4.13 3.96 3.15 2.99 2.87 8.36 7.94 7.61 6.60 6.27 6.01 51 4.88 4.64 4.44 3.40 3.23 3.09 9.26 8.80 8.43 7.24 6.88 6.59 52 5.41 5.14 4.92 3.65 3.47 3.32 10.16 9.66 9.25 7.88 7.48 7.17 53 5.94 5.64 5.41 3.90 3.71 3.55 11.07 10.52 10.07 8.51 8.09 7.74 54 6.47 6.15 5.89 4.15 3.94 3.78 11.97 11.37 10.89 9.15 8.69 8.33 55 7.00 6.65 6.37 4.40 4.18 4.00 12.87 12.23 11.72 9.79 9.31 8.91 56 7.60 7.22 6.92 4.91 4.66 4.47 13.60 12.91 12.38 10.52 9.99 9.57 57 8.20 7.79 7.46 5.42 5.15 4.93 14.32 13.61 13.04 11.24 10.68 10.23 58 8.80 8.36 8.01 5.93 5.63 5.40 15.05 14.30 13.70 11.97 11.37 10.89 59 9.40 8.93 8.55 6.44 6.12 5.86 15.77 14.98 14.36 12.69 12.06 11.55 60 10.00 9.50 9.10 6.95 6.60 6.32 16.50 15.68 15.02 13.42 12.75 12.21 61 11.60 11.02 10.56 7.86 7.47 7.15 18.70 17.77 17.02 14.87 14.12 13.53 62 13.20 12.54 12.01 8.77 8.33 7.98 20.90 19.86 19.02 16.32 15.51 14.85 Add policy fee of \$75 per year Semi-annual payment (multiply annual premium by 0.52) Monthly payment (multiply annual premium by 0.09)
• Chapter 1 Personal Finance 15 Table 2 Whole-Life Insurance Annual Whole-Life Premium Male Female Male Female Male Female Non-Smoker Non-Smoker Smoker Smoker Under 18 Under 18 Issue Rate Issue Rate Issue Rate Issue Rate Issue Rate Issue Rate per \$1,000 per \$1,000 per \$1,000 per \$1,000 per \$1,000 per \$1,000 Issue Premium Premium Premium Premium Issue Issue Premium Premium Issue Age Rate Rate Rate Rate Age Age Rate Rate Age 18 3.50 2.82 4.31 3.13 18 0 1.75 1.53 0 19 3.54 2.85 4.41 3.20 19 1 1.78 1.56 1 20 3.60 2.89 4.51 3.26 20 2 1.80 1.59 2 21 3.96 3.04 4.72 3.44 21 3 1.89 1.63 3 22 4.07 3.20 4.93 3.62 22 4 1.98 1.67 4 23 4.17 3.35 5.15 3.81 23 5 2.05 1.71 5 24 4.28 3.51 5.36 3.99 24 6 2.12 1.75 6 25 4.38 3.66 5.57 4.17 25 7 2.24 1.82 7 26 4.61 3.86 5.88 4.41 26 8 2.35 1.89 8 27 4.82 4.05 6.19 4.66 27 9 2.47 1.97 9 28 5.05 4.25 6.49 4.90 28 10 2.58 2.05 10 29 5.26 4.44 6.80 5.15 29 11 2.71 2.16 11 30 5.46 4.64 7.11 5.39 30 12 2.83 2.27 12 31 5.76 4.90 7.56 5.72 31 13 3.01 2.34 13 32 6.03 5.16 8.01 6.04 32 14 3.19 2.41 14 33 6.30 5.41 8.45 6.37 33 15 3.31 2.50 15 34 6.59 5.67 8.90 6.69 34 16 3.42 2.58 16 35 7.11 5.93 9.35 7.02 35 17 3.46 2.66 17 36 7.32 6.31 10.04 7.50 36 37 7.78 6.70 10.74 7.98 37 38 8.25 7.08 11.43 8.47 38 39 8.71 7.47 12.13 8.95 39 40 9.28 7.85 12.82 9.43 40 41 9.75 8.42 13.86 10.14 41 42 10.32 8.99 14.90 10.85 42 43 10.90 9.55 15.95 11.55 43 44 11.48 10.12 16.99 12.26 44 45 12.40 10.69 18.03 12.97 45 46 12.81 11.21 19.15 13.68 46 47 13.55 11.73 20.26 14.38 47 48 14.28 12.26 21.38 15.09 48 49 15.02 12.78 22.49 15.79 49 50 16.34 13.30 23.61 16.50 50 51 16.70 14.03 25.06 17.44 51 52 17.63 14.76 26.52 18.38 52 53 18.56 15.49 27.97 19.32 53 54 19.51 16.22 29.43 20.26 54 55 21.15 16.95 30.88 21.20 55 56 21.79 17.93 32.73 22.39 56 57 23.17 18.91 34.57 23.58 57 58 24.53 19.89 36.42 24.78 58 59 25.89 20.87 38.26 25.97 59 60 27.70 21.85 40.11 27.16 60 61 29.32 23.21 42.40 28.71 61 62 31.39 24.57 44.70 30.25 62 Add policy fee of \$75 per year Semi-annual payment (multiply annual premium by 0.52) Monthly payment (multiply annual premium by 0.09)
• 16 Essentials of Mathematics 12 Table 3 Cash Surrender Values Whole-Life Insurance Male Female Cash Surrender Value per \$1,000 of Insurance Cash Surrender Value per \$1,000 of Insurance Issue Age Policy Issue Age 20 25 30 35 40 45 50 55 60 65 70 Year 20 25 30 35 40 45 50 55 60 65 70 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 1 1 1 2 3 5 7 9 11 15 18 4 1 1 1 1 2 4 5 7 9 12 16 2 3 4 6 8 14 18 23 28 35 41 5 1 2 3 5 7 11 14 19 24 30 37 4 6 8 11 14 23 29 36 44 54 64 6 3 4 6 8 11 18 23 30 38 48 58 6 8 11 15 20 32 40 50 61 74 87 7 4 6 9 12 16 25 33 42 52 65 79 7 10 14 19 25 40 51 64 78 94 110 8 6 8 11 15 20 32 42 53 67 83 100 8 13 18 24 30 49 62 77 94 113 133 9 7 10 14 19 24 40 51 65 81 100 121 10 15 21 28 36 58 73 91 111 133 156 10 9 12 16 22 29 47 60 76 95 118 142 14 21 29 38 52 91 109 130 152 175 201 11 12 17 23 30 42 75 91 111 133 158 186 17 27 37 48 68 124 145 168 193 218 245 12 15 22 29 38 55 103 122 146 171 199 231 21 34 44 58 83 157 181 207 234 260 290 13 18 27 36 46 68 131 154 181 208 239 275 24 40 52 68 99 190 217 246 275 303 335 14 20 32 42 55 81 160 185 216 246 280 319 28 46 60 78 115 223 252 284 316 345 380 15 23 37 49 63 94 188 216 251 284 320 364 33 54 73 94 141 256 288 323 356 387 424 16 28 44 59 76 116 216 247 285 321 361 408 39 62 86 110 167 289 324 362 397 430 469 17 32 50 70 89 138 244 278 320 359 401 453 44 69 99 126 193 322 360 401 438 472 514 18 37 56 80 103 159 273 310 355 397 442 497 50 77 112 142 219 355 396 439 479 515 558 19 41 63 91 116 181 301 341 390 434 482 542 55 85 125 158 245 388 432 478 520 557 603 20 46 69 102 129 203 329 372 425 472 523 586 63 96 140 181 284 405 451 499 544 587 626 21 52 78 114 149 237 348 393 448 498 555 627 71 107 154 204 324 423 470 520 568 616 650 22 59 87 126 168 272 367 414 471 525 587 669 78 117 169 226 363 440 489 541 592 646 673 23 65 96 138 188 306 387 435 494 551 618 710 86 128 183 249 403 458 508 562 616 675 698 24 71 105 151 207 341 406 456 517 578 650 752 94 139 196 272 442 475 527 582 640 705 726 25 78 114 163 226 375 425 477 540 604 682 793 105 154 217 312 458 493 546 603 664 734 756 26 87 126 179 262 393 444 498 563 630 714 834 116 168 236 353 474 510 565 624 688 764 794 27 96 139 195 297 411 163 519 586 657 746 876 127 183 254 393 490 528 583 645 712 793 841 28 105 151 212 332 429 482 539 609 683 777 917 138 197 273 434 506 545 602 666 736 823 906 29 114 163 228 367 446 502 560 632 710 809 959 149 212 292 474 522 563 621 687 760 852 1,000 30 124 176 244 402 464 521 581 655 736 841 1,000 164 231 333 489 538 580 640 708 784 882 - 31 136 192 276 419 482 540 602 678 762 873 - 179 250 374 504 554 598 659 729 808 911 - 32 149 209 306 436 500 559 623 701 789 905 - 193 269 415 519 570 615 678 749 832 941 - 33 161 225 340 453 518 578 644 724 815 936 - 208 288 456 534 585 633 697 770 856 970 - 34 174 241 372 470 536 597 665 747 842 968 - 223 307 497 549 601 650 716 791 880 1,000 - 35 186 258 404 487 554 617 686 770 868 1,000 - 242 348 511 564 617 668 735 812 904 - - 36 202 287 421 505 571 636 707 796 894 - - 261 389 526 579 633 685 754 833 928 - - 37 219 316 438 522 589 655 728 816 921 - - 280 429 540 594 649 703 773 854 952 - - 38 235 345 455 539 607 674 749 839 947 - - 299 470 554 609 665 720 792 875 976 - - 39 252 375 472 556 625 693 770 862 974 - - 318 511 569 624 681 738 811 896 1,000 - - 40 268 404 489 573 643 712 791 885 1,000 - -
• Chapter 1 Personal Finance 17 Table 3 Cash Surrender Values Whole-Life Insurance Male Female Cash Surrender Value per \$1,000 of Insurance Cash Surrender Value per \$1,000 of Insurance Issue Age Policy Issue Age 20 25 30 35 40 45 50 55 60 65 70 Year 20 25 30 35 40 45 50 55 60 65 70 357 525 583 639 697 755 830 916 - - - 41 295 421 506 590 661 732 812 906 - - - 395 539 596 654 713 773 849 937 - - - 42 322 438 523 607 679 751 833 931 - - - 434 553 612 669 729 790 867 958 - - - 43 350 455 540 624 696 770 853 954 - - - 472 567 626 684 745 808 886 979 - - - 44 377 472 557 641 714 789 874 977 - - - 511 581 641 699 761 825 905 1,000 - - - 45 404 489 574 658 732 806 895 1,000 - - - 525 595 655 714 777 843 924 - - - - 46 421 506 591 675 750 827 916 - - - - 539 609 669 729 793 860 943 - - - - 47 438 523 608 692 768 847 937 - - - - 553 623 684 745 809 878 962 - - - - 48 455 540 625 710 786 866 958 - - - - 567 637 698 760 825 895 961 - - - - 49 472 557 642 727 804 885 979 - - - - 581 651 713 775 841 913 1,000 - - - - 50 489 574 659 744 821 904 1,000 - - - - 595 665 727 790 857 930 - - - - - 51 506 591 676 761 839 923 - - - - - 609 679 741 805 872 948 - - - - - 52 523 608 693 778 857 942 - - - - - 623 693 756 820 888 965 - - - - - 53 540 625 711 795 875 962 - - - - - 637 707 770 835 904 983 - - - - - 54 557 642 728 812 893 981 - - - - - 651 721 784 850 920 1,000 - - - - - 55 574 659 745 829 911 1,000 - - - - - 665 735 799 865 936 - - - - - - 56 591 676 762 846 929 - - - - - - 679 749 813 880 952 - - - - - - 57 608 693 779 863 946 - - - - - - 693 762 828 895 968 - - - - - - 58 625 711 796 880 964 - - - - - - 707 776 842 910 984 - - - - - - 59 642 728 813 897 962 - - - - - - 721 790 856 925 1,000 - - - - - - 60 659 745 830 915 1,000 - - - - - - 735 804 871 940 - - - - - - - 61 676 762 847 932 - - - - - - - 749 818 885 955 - - - - - - - 62 693 779 864 949 - - - - - - - 762 832 899 970 - - - - - - - 63 711 796 881 966 - - - - - - - 776 846 914 985 - - - - - - - 64 728 813 896 983 - - - - - - - 790 860 928 1,000 - - - - - - - 65 745 830 915 1,000 - - - - - - - 804 874 943 - - - - - - - - 66 762 847 932 - - - - - - - 818 888 957 - - - - - - - - 67 779 864 949 - - - - - - - - 832 902 971 - - - - - - - - 68 796 881 966 - - - - - - - - 846 916 986 - - - - - - - - 69 813 898 983 - - - - - - - - 860 930 1,000 - - - - - - - - 70 830 915 1,000 - - - - - - - - 874 944 - - - - - - - - - 71 847 932 - - - - - - - - - 888 958 - - - - - - - - - 72 864 949 - - - - - - - - - 902 972 - - - - - - - - - 73 881 966 - - - - - - - - - 916 986 - - - - - - - - - 74 896 983 - - - - - - - - - 930 1,000 - - - - - - - - - 75 915 1,000 - - - - - - - - - 944 - - - - - - - - - - 76 932 - - - - - - - - - - 958 - - - - - - - - - - 77 949 - - - - - - - - - - 972 - - - - - - - - - - 78 966 - - - - - - - - - - 986 - - - - - - - - - - 79 983 - - - - - - - - - - 1,000 - - - - - - - - - - 80 1,000 - - - - - - - - - - Every effort has been made to ensure the accuracy of the above values, but accuracy is not guaranteed. In the event of a discrepancy, the insurance policy governs.
• 18 Essentials of Mathematics 12 Example 1 Jason Rettinger is a 32-year-old male non-smoker. He wants to purchase a 10-year term life insurance policy worth \$120,000. Find his annual premium, and then find his monthly premium. Solution Look in the Ten-Year Term Life Insurance table for a 32-year-old male non-smoker. Be sure to select the first column in the male non-smoker section, since the next column is the rate for policies between \$250,000 and \$499,999. The premium for Jason would be \$1.02 per thousand dollars of coverage. The easiest way to calculate his annual premium is: \$1.02 \$120,000 \$122,400 \$1,000 \$1,000 \$122.40 Now add the \$75 policy fee (see Table 1 footnote): \$122.40 \$75.00 \$197.40 (annual premium) To find the monthly premium, multiply the annual premium by 0.09: \$197.40 0.09 \$17.77 (rounded) Jason pays \$17.77 per month for his life insurance. If Jason decides to pay monthly premiums, the total cost over the year would be \$213.24 (\$17.77 12). Compared to paying one annual payment of \$197.40, this is an additional cost of \$15.84 to cover the handling of his account.
• Chapter 1 Personal Finance 19 Example 2 Lynne is a 20-year-old non-smoking female who wishes to purchase a whole-life policy worth \$75,000. Find her premiums if she decides to make semi-annual payments. Solution Use the Whole-Life Insurance table, and look for the column for non- smoking females. Sliding down to 20-year-olds, and going across to the appropriate column, you will see a rate of \$2.89 per thousand dollars of coverage. \$2.89 \$75,000 \$1,000 \$216.75 Remember to add the policy fee \$216.75 \$75.00 \$291.75 Now use the footnote on this table to calculate the amount for semi- annual payments. Multiply the annual premium by 0.52: \$291.75 0.52 \$151.71 Lynne pays \$151.71 semi-annually for her life insurance.
• 20 Essentials of Mathematics 12 Example 3 Wayne is 22 years old and he smokes. He is considering purchasing a 10- year term insurance policy in the amount of \$200,000. His agent advises him that if he quits smoking, the insurance will be much less expensive. Calculate the difference in the annual premiums if Wayne were to quit smoking. Solution 22-year-old Male Smoker 22-year-old Male Non-Smoker \$1.43 \$200,000 \$0.85 \$200,000 \$1,000 \$286.00 \$1,000 \$170.00 \$286.00 \$75.00 \$361.00 \$170.00 \$75.00 \$245.00 Subtract to find the difference in annual premiums: \$361.00 \$245.00 \$116.00 Class Discussion Discuss why smokers have to pay more for life insurance than non- smokers. Why do men have to pay more for life insurance than women?
• Chapter 1 Personal Finance 21 Example 4 Jim Chow bought a \$50,000 whole-life policy when he was 20 years old. When he turned 50, he decided to cancel his insurance and take the cash surrender value. How much did he receive? Solution Use the Cash Surrender Values table. Find the issue age of 20 in the “Male” column. Since Jim had this policy for 30 years (50 20 30), slide down the column labelled “Policy Year” to 30. You should see a value of \$149 per thousand dollars. \$50,000 \$149.00 \$1,000 \$7,450.00 The cash surrender value of Jim’s policy is \$7,450.00 Class Activity As a class, research the rates of several companies that offer life insurance. Assume you are a 20-year-old and that you wish to buy \$100,000 of whole-life insurance. Find the total monthly premiums for the following cases: • male smoker • male non-smoker • female smoker • female non-smoker The class should compile a table that lists the companies and the rates they would charge. Which company would your class select? List the reason(s) why you chose that company.
• 22 Essentials of Mathematics 12 Notebook Assignment 1. Denise Gill is a 33-year-old non-smoker. What will her annual premium be for a \$100,000, 10-year term life insurance policy? 2. Kevin Wong is 30 years old and smokes. Calculate his annual premium for a \$50,000 whole-life policy. 3. Harry and Sally Heller are both 25 years old, and non-smokers. They each decide to purchase \$200,000 whole-life insurance policies. a) Find the monthly premium each will have to pay. b) Why does Harry have to pay more than Sally? 4. Howard was 25 years old when he bought an \$80,000 whole-life insurance policy. At the age of 60, he decided to cancel his policy and take the cash surrender value. a) How much money can he expect back? b) List 2 reasons why someone might choose term life insurance instead of whole-life. c) List 2 reasons why someone might choose whole-life insurance instead of term. 5. Luen is comparing the insurance costs of smokers and non-smokers. He selects a 27-year-old male, and picks \$300,000 insurance over a 10-year term. a) Find the annual premium for a smoker and a non-smoker. b) What is the difference in the premiums? c) Find the percent difference compared to the non-smoking rate. 6. Malvina Antoniak is a 25-year-old smoker. What is her semi-annual premium for \$270,000 of whole-life insurance? 7. A man buys a \$60,000, 10-year term life insurance policy when he is 28. If he dies when he is 39, how much will his beneficiary collect?
• Chapter 1 Personal Finance 23 Extension 8. Twin girls have decided to purchase \$260,000 of life insurance on their twentieth birthday. One buys 10-year term life insurance, while the other decides to purchase whole-life insurance. Both are non- smokers. a) Determine the total cost of premiums that each would pay over 40 years. The 10-year term life policy is renewable after each 10- year period, but at the new rates for this twin’s age. b) Find the cash surrender value after 40 years. c) Which twin selected the better coverage? Explain your reasoning. An insurance salesperson explains the various types of life insurance.
• Chapter 1 Personal Finance 25 First-time home buyers can usually secure financing with only 5% of the purchase price as a down payment. The National Housing Act requires that all mortgages with less than a 25% down payment be insured against loss. People who need mortgages over 75% of the principal are required to pay a higher rate (between 0.5% and 3.75% higher). Many different types of mortgages are available from financial institutions. This exploration will look at some of them briefly, but will focus on fixed-rate, closed mortgages. Career Connection Name: Phili ppe Gagnon Job: insuran ce adjuster Current sala ry: \$2,000 p er month Education: grade 12; co through Insu urses rance Institute Canada of Career goa l: branch man an insurance ager at company off ice Keyword se arch: Canad courses insura a nce adjuster New Terms closed mortgage: a mortgage which does not allow payments on the principal. fixed-rate mortgage: a mortgage with the interest rate locked in for a specified period of time.
• 26 Essentials of Mathematics 12 Types of Mortgages Fixed-rate mortgages can be negotiated with a financial institution for any number of years. These mortgages guarantee the monthly payment for the selected term (for example, 2 years). With a fixed rate, you are able to budget your mortgage payments and are protected from any spikes in interest rates. Usually this type of mortgage is locked in, and you would be charged a penalty to pay extra on the principal, or to pay it off before the end of the term. However, some fixed-rate mortgages allow for an extra payment annually. Variable-rate mortgages are popular with people who believe the interest rates are going to fall or remain constant. If the rates fall, the amount of interest charged each month against the principal borrowed will be less. You can still budget your mortgage payment, which stays constant. These mortgages are usually considered to be open, and you can pay against the principal at any time and can close the mortgage without penalty. If the rates go up suddenly, you may want to switch over to a fixed-rate mortgage to protect yourself. Technology New Terms Information about mortgages can be open mortgage: a mortgage that found through a financial institution’s allows additional payments on the web site or from : principal. www.canadamortgage.com variable-rate mortgage: a mortgage or www.cba.ca where the interest rate may change from month to month. Many web sites contain financial tools and calculators relating to mortgages. Banking laws, including mortgages, are different in Canada than in other countries. Canadian web sites should be used.
• Chapter 1 Personal Finance 27 Table 4 Amortization Table Blended Payment of Principal and Interest per \$1,000 of Loan Interest Rate 5 Years 10 Years 15 Years 20 Years 25 Years 4.00% 18.40 10.11 7.38 6.04 5.26 4.25 18.51 10.23 7.50 6.17 5.40 4.50 18.62 10.34 7.63 6.30 5.53 4.75 18.74 10.46 7.75 6.44 5.67 5.00 18.85 10.58 7.88 6.57 5.82 5.25 18.96 10.70 8.01 6.71 5.96 5.50 19.07 10.82 8.14 6.84 6.10 5.75 19.19 10.94 8.27 6.98 6.25 6.00 19.30 11.07 8.40 7.12 6.40 6.25 19.41 11.19 8.53 7.26 6.55 6.50 19.53 11.31 8.66 7.41 6.70 6.75 19.64 11.43 8.80 7.55 6.85 7.00 19.75 11.56 8.93 7.70 7.00 7.25 19.87 11.68 9.07 7.84 7.16 7.50 19.98 11.81 9.21 7.99 7.32 7.75 20.10 11.94 9.34 8.13 7.47 8.00 20.21 12.06 9.48 8.28 7.63 8.25 20.33 12.19 9.62 8.43 7.79 8.50 20.45 12.32 9.76 8.59 7.95 8.75 20.56 12.45 9.90 8.74 8.12 9.00 20.68 12.58 10.05 8.89 8.28 9.25 20.80 12.71 10.19 9.05 8.44 9.50 20.91 12.84 10.33 9.20 8.61 9.75 21.03 12.97 10.48 9.36 8.78 10.00 21.15 13.10 10.62 9.52 8.94 10.25 21.27 13.24 10.77 9.68 9.11 10.50 21.38 13.37 10.92 9.84 9.28 10.75 21.50 13.50 11.06 9.99 9.45 11.00 21.62 13.64 11.21 10.16 9.63 11.25 21.74 13.77 11.36 10.32 9.80 11.50 21.86 13.91 11.51 10.48 9.97 11.75 21.98 14.04 11.66 10.65 10.14 12.00 22.10 14.18 11.82 10.81 10.32 12.25 22.22 14.32 11.97 10.98 10.49 12.50 22.34 14.46 12.12 11.14 10.67 12.75 22.46 14.59 12.28 11.31 10.85 13.00 22.58 14.73 12.43 11.48 11.02 13.25 22.70 14.87 12.59 11.64 11.20 13.50 22.82 15.01 12.74 11.81 11.38 13.75 22.94 15.15 12.90 11.98 11.56 14.00 23.07 15.29 13.06 12.15 11.74 14.25 23.19 15.43 13.21 12.32 11.92 14.50 23.31 15.58 13.37 12.49 12.10 14.75 23.43 15.72 13.53 12.67 12.28 15.00 23.56 15.86 13.69 12.84 12.46
• 28 Essentials of Mathematics 12 In order to complete an amortization schedule, you will need to determine the monthly payment from an amortization table. You will need to calculate the owner’s equity, unpaid balance, interest on unpaid balance, principal, and the owner’s new equity. Below are the six simple steps. Complete them in order for as many monthly payments as the schedule requires. 1. Calculate the monthly payment using the amortization table on page 27. Then write in the unpaid balance and the owner’s equity. 2. To find the interest payment, multiply the unpaid balance by the interest rate and divide by 12. 3. Subtract the interest from the monthly payment to find the principal payment. 4. Add the principal payment to the owner’s equity. 5. Subtract the principal payment from the unpaid balance. 6. Repeat for as many months as required. The table below is a useful way to organize your information. Owner’s Unpaid Monthly Interest Principal Equity Balance Payment Payment Payment PLE SAM Technology Spreadsheet software can be used to calculate amortization schedules. You may also use a search engine such as Google or Altavista and type in “amortization table.” You will be able to access many financial calculator programs that are available on-line.
• Chapter 1 Personal Finance 29 The following example illustrates these steps. Example 1 Write an amortization schedule for three months, given a mortgage of \$85,000 (after a \$20,000 down payment), at 6% over 20 years. Solution 1. First, write the unpaid balance (the amount actually borrowed) and the owner’s equity (or down payment) in first line of the table. Calculate the monthly payment using the amortization table: 6% over 20 years is \$7.12 per \$1,000 borrowed \$7.12 \$85,000 \$1,000 \$605.20/month 2. Unpaid balance multiplied by interest rate divided by 12 gives the interest: \$85,000 0.06 —— \$425.00/month 12 months 3. Monthly payment minus the interest gives the principal: \$605.20 \$425.00 \$180.20 4. Add this principal to the owner’s equity: \$20,000 \$180.20 \$20,180.20 5. Subtract the principal amount from the unpaid balance to give the new unpaid balance: \$85,000 \$180.20 \$84,819.80 6. Go back to step 2. Repeat these steps to complete the schedule for the next two months: Owner’s Unpaid Monthly Interest Principal Equity Balance Payment Payment Payment 1 1 \$20,000 \$85,000 \$605.20 \$20,180.20 4 \$84,819.80 5 \$605.20 \$425.00 2 \$180.20 3 \$20,361.30 \$84,638.70 \$605.20 \$424.10 \$181.10 \$20,543.31 \$84,456.69 \$605.20 \$423.19 \$182.01
• 30 Essentials of Mathematics 12 Example 2 Mr. and Mrs. Smith purchased a home for \$160,000. They made a down payment of \$35,000. If they negotiated a mortgage at 7 1 % over 25 years, 4 calculate: a) the amount they would need to borrow for the mortgage b) the monthly mortgage payment c) the amount of interest on the first payment d) the amount of interest they would pay over the life of the mortgage Solution a) \$160,000 is the purchase price of the home. If the Smiths made a down payment of \$35,000, they would need to borrow the balance: \$160,000 \$35,000 \$125,000 They would borrow \$125,000. b) Find 7 1 % in the amortization table. A rate of 7 1 % over 25 years 4 4 requires a payment of \$7.16 per \$1,000 borrowed: \$7.16 x \$125,000 \$895.00 \$1,000 The monthly payment would be \$895.00. c) To find the amount of interest on the first payment, multiply the balance by the rate and divide by 12 months: \$125,000 0.0725 ——— 12 \$755.21 The Smiths will pay \$755.21 in interest on their first payment. d) To find the total amount of interest they will pay over the life of the mortgage, multiply the monthly payment by the number of months and subtract the principal borrowed: monthly payment number of months principal borrowed total interest paid \$895 12 months 25 years \$268,500 \$268,500 \$125,000 \$143,500 Over the life of the mortgage, the Smiths will pay \$143,500 in interest.
• Chapter 1 Personal Finance 31 Project Activity You must find a home to purchase. Assume that you have an inheritance of \$30,000 to use as a down payment on your home. Use local real estate figures or data from www.mls.ca. Assume that you and your partner are earning a gross family income of \$65,000. Describe the home you want to purchase. Then find three providers of mortgage money, and justify why you would select one over the others. Include your data on mortgages. Finding a home that you can afford may be a challenge. Mental Math Determine the monthly mortgage payment: a) \$6.50 per \$1,000 for \$100,000 b) \$5.00 per \$1,000 for \$120,000 c) \$4.00 per \$1,000 for \$150,000
• 32 Essentials of Mathematics 12 Notebook Assignment 1. Find the monthly payments on the following mortgages: a) \$50,000 at 5.5% over 15 years b) \$85,000 at 6 —1—% over 25 years 2 c) \$182,250 at 7 —1—% over 15 years 2 d) \$78,380 at 6% over 10 years 2. Kevin McIlwraith is considering purchasing a condominium in North Vancouver for \$149,750. He has \$55,500 saved for a down payment. The credit union is offering him a mortgage at 5.5% over 20 years. Find his monthly payment including principal and interest. 3. A \$70,000 mortgage was offered by a loans officer at a rate of 6% over 20 years. How much interest would be paid over the life of the mortgage? 4. Create an amortization schedule showing the principal and interest over the first four months of an \$80,000 mortgage at 7 —1—% over 20 2 years, with a \$15,000 down payment. Assume monthly payments. 5. Explain why you might consider taking out a mortgage with a higher monthly payment over a shorter amortization period. 6. Pierre LaFrance is considering both a variable-rate and a fixed-rate mortgage. List two advantages to each. Which would you recommend, and why? 7. Sam Tamaki has two bank offers to consider for his \$105,500 mortgage. One option is at 7% over 20 years, while the other is at 6% over 25 years. Calculate the amount of interest he would pay over the life of each mortgage. Show which would be the better choice if payments are made monthly.
• Chapter 1 Personal Finance 33 Extension 8. Mila Obradovic wants to purchase a home costing \$180,000. She has \$40,000 saved up for the down payment. The bank will only finance \$110,000 at 7 —1—% over 25 years. She has arranged a second mortgage 2 through her family at 9% over 20 years for the balance. Find the total monthly mortgage payments she will be making. Paying off a mortgage for a large house such as this one in Arviat, Nunavut, will often take 25 years.
• 34 Essentials of Mathematics 12 Exploration 3 Exploring Mortgage Payments This exploration is designed to encourage you to look at mortgage options other than the conventional monthly “fixed-rate” mortgages studied in the previous exploration. You will explore various payment options for mortgages, and will be asked to make decisions involving budgetary concerns with shorter amortization periods, bi-weekly payments, weekly payments, and annual contributions. A basic mortgage of \$125,000 at 7 1 % over 25 years will cost 4 \$143,500 in interest. There are a few payment options you should consider that can dramatically reduce the amount of interest you have to pay. Using an on-line financial calculator or a spreadsheet program can make it much easier to compare different situations. Payment Options a) semi-monthly: this saves very little over the life of the mortgage. The monthly payment is simply divided into halves. b) accelerated bi-weekly: this option can save you many thousands of dollars. It takes your monthly payment and divides it by two to make it bi-weekly. But, there are 52 weeks in a year, and therefore 26 bi-weekly payments. As a result, you would make an additional two payments per year, reducing your principal more quickly, and lowering the total interest you have to pay. This option is especially advantageous for those who get paid bi-weekly. Goals In this exploration, you will examine various mortgage payment plans and make decisions about the best way to pay off a mortgage.
• Chapter 1 Personal Finance 35 c) accelerated weekly: this option can save slightly more. It takes your monthly payment and divides it by four to find a weekly payment. But, with 52 weeks in a year, you are making four additional payments when compared to the monthly amount. This reduces your principal faster, and lowers the amount of interest paid. d) double-up: some lending institutions offer a “double-up” plan where you are allowed to pay double your usual amount on one or more occasions during the year. This extra payment goes directly against the principal. e) lump sum: on the anniversary of your mortgage, or the renewal date, you may be allowed to pay a “lump sum.” This goes directly against your principal, and reduces the amount of interest considerably. f) shorter amortization periods: although the monthly payments are higher, you can save thousands over the life of the mortgage. The figures in the table below were obtained from an on-line mortgage calculator. The table shows the effect of different payment options on a \$142,772.35 mortgage amortized over 25 years at 7%. Comparison of Mortgage Amortization Periods Payment Payment Amort. Interest Interest Schedule Amount (years) Paid Saved Monthly \$1,000.00 25 \$157,227 0 Accelerated \$500.00 20.58 \$124,353 \$32,874 Bi-weekly Accelerated \$250.00 20.52 \$123,849 \$33,378 Weekly Note: figures may vary slightly depending on the financial institution. By making accelerated bi-weekly payments, \$32,874 is saved and the mortgage amortization period is reduced from 25 years to 20.58 years. By paying weekly, \$33,378 is saved and the mortgage amortization period is reduced from 25 years to 20.52 years.
• 36 Essentials of Mathematics 12 Example 1 Nancy Moreau is comparing mortgages at her financial institution. The loans officer wants her to accept a 25-year amortization period because it has a much lower monthly payment. But Nancy thinks she can pay the mortgage off sooner. This will save her many thousands of dollars. The mortgage is \$130,000 at 6 —1—%. Nancy wants to pay it off over 15 years. 2 Determine the amount of interest she would save if the loan were amortized over 15 years instead of 25 years. Solution Find the monthly payments for both situations: 1 1 6 % over 25 years 6 % over 15 years 2 2 \$6.70 \$130,000 \$8.66 \$130,000 \$1,000 \$871.00/month \$1,125.80/month \$1,000 Total interest paid over life of the mortgage: \$871 12 25 \$261,300 \$1125.80 12 15 \$202,644 \$261,300 \$130,000 \$131,300 \$202,644 \$130,000 \$72,644 The difference is: \$131,300 \$72,644 \$58,656 Even though the monthly payments are higher, a shorter amortization period reduces the borrowing costs over the life of the mortgage.
• Chapter 1 Personal Finance 37 Example 2 Jillian is considering mortgage options. Her monthly payment over 20 years will be \$593.96 on a \$90,000 mortgage at 5% (using a mortgage calculator). If she converts this to accelerated bi-weekly payments, her mortgage will be paid off in 17.7 years. a) Find the amount of her accelerated bi-weekly payments. b) How much would this save her in interest charges over the life of the mortgage? c) How much extra would she pay in a year? Solution a) \$593.96 2 \$296.98 b) Monthly Payments: \$593.96 12 20 \$142,550.40 \$142,550.40 \$90,000 \$52,550.40 Accelerated Bi-weekly Payments: \$296.98 26 17.7 \$136,670.20 \$136,670.20 \$90,000 \$46,670.20 Total Saved: \$52,550.40 \$46,670.20 \$5,880.20 c) \$296.98 26 \$7,721.48 \$593.96 12 \$7,127.52 \$7,721.48 \$7,127.52 \$593.96 Note that this amount is one month’s mortgage payment. You can see clearly that the mortgage will be paid off sooner with the accelerated bi-weekly payments. Also, the amount of interest paid over the life of the mortgage is substantially reduced.
• 38 Essentials of Mathematics 12 Example 3 Liam is researching his options on a mortgage of \$120,000 at 6% over 25 years. Using an on-line mortgage calculator, find: a) the monthly payment b) the accelerated bi-weekly payment c) the amount of interest saved if he chooses the bi-weekly option. Solution Using a mortgage calculator, you find that by paying bi-weekly, Liam can save \$20,636 and shorten the amortization period from 25 years to 21 years. Accelerated Payments Monthly Payments Bi-weekly Mortgage Amount \$120,000 \$120,000 Interest Rate 6% 6% a b Payment \$773.15 \$386.58 Years to Repay 25 21 Total Interest \$111,949 \$91,313 c Interest Savings \$20,636 continued on the next page
• Chapter 1 Personal Finance 39 Mortgage Payoff Schedule Monthly Payments Accelerated Bi-weekly Payments Year Payments Balance Payments Balance \$120,000 \$120,000 1 \$9,278 \$117,864 \$10,051 \$117,065 2 \$9,278 \$115,596 \$10,051 \$113,949 3 \$9,278 \$113,189 \$10,051 \$110,640 4 \$9,278 \$110,632 \$10,051 \$107,127 5 \$9,278 \$107,919 \$10,051 \$103,398 6 \$9,278 \$105,038 \$10,051 \$99,437 7 \$9,278 \$101,979 \$10,051 \$95,232 8 \$9,278 \$98,731 \$10,051 \$90,768 9 \$9,278 \$95,283 \$10,051 \$86,028 10 \$9,278 \$91,623 \$10,051 \$80,994 11 \$9,278 \$87,736 \$10,051 \$75,650 12 \$9,278 \$83,610 \$10,051 \$69,976 13 \$9,278 \$79,230 \$10,051 \$63,952 14 \$9,278 \$74,597 \$10,051 \$57,55 15 \$9,278 \$69,642 \$10,051 \$50,764 16 \$9,278 \$64,400 \$10,051 \$43,553 17 \$9,278 \$58,853 \$10,051 \$35,896 18 \$9,278 \$52,926 \$10,051 \$27,767 19 \$9,278 \$46,653 \$10,051 \$19,135 20 \$9,278 \$39,993 \$10,051 \$9,971 21 \$9,278 \$32,293 \$10,051 \$240 22 \$9,278 \$25,416 \$241 \$0 23 \$9,278 \$17,446 \$0 \$0 24 \$9,278 \$8,985 \$0 \$0 25 \$9,279 \$0 \$0 \$0
• 40 Essentials of Mathematics 12 Example 4 Debbie Webb is on a very restricted budget. Her mortgage is \$100,000 at 5% for 20 years. Her take-home pay is \$2,200 per month. Since no more than 30% of her pay should be dedicated to housing costs, can Debbie afford to move to an accelerated bi-weekly option? Solution Debbie’s monthly dedicated housing cost is limited to: \$2,200 0.3 \$660.00 Estimated Payment of Principal and Interest (using a mortgage calculator): Payment Options Payment Years to Repay Mortgage Monthly \$657.00 20 Accelerated Bi-weekly \$328.56 17.43 \$328.56 26 —— 12 \$711.88 So, Debbie could not afford the accelerated bi-weekly payments within the parameters of her budget . Project Activity Create a spreadsheet showing the amortization schedule of payments for your home. Include monthly, accelerated bi- weekly, and accelerated weekly options, showing the amount of interest you will have to pay over the life of the mortgage.
• Chapter 1 Personal Finance 41 Notebook Assignment 1. Bev Joyce is thinking of purchasing a home worth \$140,000. She has \$40,000 saved up for the down payment. Her mortgage is at 4.75% over 25 years. Use an on-line mortgage calculator or a spreadsheet program to determine: a) her monthly payment b) if she chose the accelerated bi-weekly option, how much she would save in interest. 2. Yvette Beaulieu has secured a mortgage of \$120,000 at 6% over 20 years, making monthly payments. Her lending institution will allow her to double-up one payment per year. a) Calculate her monthly payment. b) Calculate the amount of interest she will pay over the life of the mortgage. c) Use a spreadsheet to determine the effect of her double-up payments on the interest. 3. Marcel Pelletier is paying \$750 per month towards his mortgage. His monthly take-home pay is \$2,500. Other budget items are: food and utilities, \$600; car expenses, \$400; entertainment expenses, \$400; and savings, \$350. With his mortgage renewal date coming in a year, he has the option to pay a lump sum towards the principal. How would you suggest he alter his budget, and by how much, to save up for this extra payment? 4. Mona Katsumoko is paid on a weekly basis. She presently has a mortgage of \$65,000 at 7% amortized over 15 years. The monthly mortgage payment is \$580.45. Determine: a) the amount of interest she will pay over the life of the mortgage b) the amount her payments would be if she exercised the accelerated weekly payment option c) when the mortgage would be paid out if she made accelerated weekly payments d) the amount of interest she would save by making accelerated weekly payments.
• 42 Essentials of Mathematics 12 Problem Analysis Number Patterns Pattern 1 Choose any number from 2 to 9. Multiply it by 41. Multiply the result by 271. Try this with several one-digit numbers. What do you notice about the result? Why does this work? Pattern 2 Select any three-digit number, for example: 123. Repeat the digits to get a six-digit number: 123,123. Divide this number by 13, then by 11, then by 7. What did you get? Try this with a few more three-digit numbers. What happens? Why do you always get this result? Give an explanation. Pattern 3 12 1 112 121 1112 12321 11112 1234321 2 11111 123454321 Continue this pattern: 1111112 ______________________ 11111112 ______________________ 111111112 ______________________ 1111111112 ______________________ 11111111112 ______________________ Does the pattern continue? What happens to the pattern when you reach 11111111112 (ten 1s)? Why?
• Chapter 1 Personal Finance 43 Games A Weird Will A wealthy lawyer owned 11 expensive cars. When he died, he left a weird will. It asked that his 11 cars be divided among his three sons in a particular way. Half of the cars were to go to the eldest son, one-fourth to his middle son, and one-sixth to the youngest. Everybody was puzzled. How can 11 cars be divided in such a way? While the sons were arguing about what to do, a mathematics teacher drove up in her new sports car. “Can I be of help?” she asked. After the sons explained the situation, she parked her sports car next to the lawyer’s 11 cars and hopped out. “How many cars are there now?” The sons counted 12. Then she carried out the terms of the will. She gave half of the cars, 6, to the oldest son. The middle son got one-fourth of 12, or 3. The youngest son got one-sixth of 12, or 2. “6 plus 3 plus 2 is 11. So, one car is left over. And that’s my car.” She jumped into her sports car and drove off. “Glad to be of service!” Can you write a similar will for 17 cars?
• 44 Essentials of Mathematics 12 Exploration 4 Gross Debt Service Ratio The gross debt service ratio (GDSR) is a formula used by most financial institutions to determine whether or not you can afford the property you have selected. It starts with a general rule that total household expenses cannot exceed 32% of gross income. Your mortgage application will likely be denied if the gross debt service ratio is over 32%. Career Connection Name: Darice Whyte Job: supervisor, mortgage services Current salary: \$65,000 per year Education: grade 12; certified general accountant program Career goal: mortgage broker Keyword search: CGA Canada (www.cga-canada.org) Goals New Terms In this exploration, we will discuss the gross debt service ratio: a formula gross debt service ratio and determine used by most financial institutions to eligibility for mortgage loans. determine whether or not you can afford the property you have selected.
• Chapter 1 Personal Finance 45 The formula is calculated as follows: (monthly mortgage payment + monthly property tax monthly heating costs) gross monthly income 100 Interest Rate Factor Table* Rate Factor Rate Factor Rate Factor 6% 0.00640 8% 0.00763 10% 0.00894 6.5% 0.00670 8.5% 0.00795 10.5% 0.00928 7.0% 0.00700 9.0% 0.00828 11.0% 0.00963 7.5% 0.00732 9.5% 0.00861 11.5% 0.00997 * Based on 25-year amortization Note: the figures used in this table are mortgage payment amounts per \$1.00 rather than per \$1,000.00, as in a mortgage amortization table.
• 46 Essentials of Mathematics 12 Example 1 You would like to purchase a condominium for \$93,000. You are able to make a down payment of \$8,000. The bank will finance this property at a rate of 8—1—% over 25 years. Your gross monthly income is \$3,000. The 2 monthly property taxes are \$125 and the monthly utility costs are \$150. Calculate the monthly mortgage payment and the gross debt service ratio. Solution 8 1 % over 25 years shows \$7.95 per \$1,000 borrowed. 2 \$93,000 \$8,000 down payment \$85,000 (amount of mortgage) —,000 \$85 — \$7.95 \$1,000 \$675.75 (monthly mortgage payment) Gross debt service ratio formula: (\$675.75 \$125 \$150) \$3,000 100 31.7% Since the gross debt service ratio is under 32%, your application would likely be accepted. A condominium may be more affordable than a single family house.
• Chapter 1 Personal Finance 47 Example 2 Tom and Sarah Green want to purchase the home of their dreams in Winnipeg. They have saved \$42,500 for the down payment on a house costing \$215,750. Tom’s job pays \$2,400 per month, while Sarah has a gross monthly income of \$2,450. The mortgage company has offered them a rate of 7% over 25 years, subject to a favourable gross debt service ratio. The utility company estimates the annual costs of gas and electricity to be \$2,640, and the municipality shows the property taxes to be \$3,600 a year. Use the gross debt service ratio to determine if they qualify for this mortgage. Solution The mortgage amount will be: \$215,750 \$42,500 down payment \$173,250 The table shows that 7% over 25 years will cost \$7 per \$1,000 borrowed. \$173,250 \$7.00 —— \$1,000 \$1,212.75 The monthly payment will be \$1,212.75. The gross debt service ratio is: [\$1,212.75 (\$2,640 12) (\$3,600 12)] \$4,850 35.7% The Greens’ application would probably not be accepted. Their monthly household expenses would exceed 32% of their gross income.
• 48 Essentials of Mathematics 12 Lending institutions will ask that you complete an affordability chart to determine the size of the mortgage best suited to your financial position. The following template will help you determine the price of the home you can afford. Affordability Chart The Formula Your Calculations Gross monthly household income _______________ Multiply by 32% (GDSR) 0.32 Total affordable household expenses ______________ E Subtract SAMPL Monthly property taxes ______________ Monthly heating costs ______________ One-half of condo/strata fees (if applicable) ______________ Monthly mortgage payment your household can afford ______________ To calculate total mortgage amount, divide by the estimated interest rate factor that corresponds to your interest rate (see table on page 45) ______________ Maximum amount of mortgage you can afford ______________ Add your cash down payment ______________ Your maximum affordable price ______________ Actual mortgage payment interest rate factor actual total mortgage ______________ Gross Debt Service Ratio (actual monthly mortgage payment + monthly property taxes + monthly heating) ————————— gross monthly income 100
• Chapter 1 Personal Finance 49 Location is one of the main factors in determining the price of a house. Could this house be bought for \$145,000 where you live? Example 3 Jeremy Martin is asking the bank to approve his mortgage application. He earns \$4,400 as gross monthly income. Jeremy hopes to purchase a home using a \$120,000 mortgage amortized over 25 years at 6 1 %. He 2 has \$25,000 saved for the down payment. The annual property taxes for the home are \$2,160, and the estimated monthly heating costs are \$110. Complete the affordability chart to determine if Jeremy will be given the mortgage.
• 50 Essentials of Mathematics 12 Solution The Formula Your Calculations Gross monthly household income \$4,400 Multiply by 32% (GDSR) 0.32 Total affordable household expenses \$1,408 Subtract Monthly property taxes (\$2,160 12) \$180.00 Monthly heating costs \$110.00 One-half of condo/strata fees (if applicable) 0.00 Monthly mortgage payment your household can afford \$1,118 To calculate total mortgage amount, divide by the estimated interest rate factor that corresponds to your interest rate (see table page 45). 0.0067 Maximum amount of mortgage you can afford \$166,865.67 Add your cash down payment \$25,000 Your maximum affordable price \$191,865.67 Actual mortgage payment interest rate factor actual total mortgage \$804.00 Gross Debt Service Ratio (\$804.00 \$180.00 \$110.00) = ———— \$4,400 100 24.9% With a GDSR of 24.9%, Jeremy’s mortgage application is likely to be approved. Many lending institutions will pre-qualify you for a mortgage, and will use a form similar to the one above to calculate the maximum amount of money they will lend you for a home.
• Chapter 1 Personal Finance 51 Example 4 Gil Dhaliwal has \$12,500 saved up for a down payment. He earns about \$2,800 each month. Using a bank rate of 7%, and estimating monthly property taxes to be \$180 and monthly heating costs to be \$125, determine the maximum amount of mortgage he would be given. Solution The Formula Your Calculations Gross monthly household income \$2,800 Multiply by 32% (GDSR) 0.32 Total affordable household expenses \$896.00 Subtract Monthly property taxes \$180.00 Monthly heating costs \$125.00 One-half of condo/strata fees (if applicable) 0.00 Monthly mortgage payment your household can afford \$591.00 To calculate total mortgage amount, divide by the estimated interest rate factor that corresponds to your interest rate (see table on page 45) 0.007 Maximum amount of mortgage you can afford \$84,428.57 Add your cash down payment \$12,500 Your maximum affordable price \$96,928.57 The maximum purchase price that Gill could afford would be \$96,928.57.
• 52 Essentials of Mathematics 12 Project Activity Apply your gross earnings, mortgage payment, estimated heating costs, and estimated property tax (all monthly) to the gross debt service ratio, and see if your mortgage will be accepted. If you aspire to own a home such as this one in Vancouver, you need to set financial goals early in life.
• Chapter 1 Personal Finance 53 Notebook Assignment 1. Glen Louie wants to buy a house with a mortgage payment of \$627.50. His gross monthly earnings are \$3,100. He estimates the monthly heating costs to be \$175, and the monthly property tax to be \$185. Calculate his gross debt service ratio. 2. Lynne earns an income of \$3,500 per month. She has saved \$55,500 for a down payment on a home costing \$215,800. The heating costs will be about \$220 per month, while the monthly property tax bill is \$235. If she negotiates a mortgage at 4 1 % over 20 years, calculate 2 her gross debt service ratio. 3. Paul Laroche has a monthly income of \$3,700. His mortgage payment is \$650 per month. He estimates the annual heating costs to be \$2,520. Annual property taxes are \$2,220. Calculate Paul’s gross debt service ratio. 4. Lorna has \$22,000 saved up for a down payment. The bank is offering her a mortgage at 6% over 25 years. Her monthly gross income is \$2,950. Assuming the heating bills will be \$110 per month and the monthly property taxes \$140, find the maximum amount of mortgage the bank is willing to allow. 5. List possible reasons explaining why banks will not allow customers to budget more than 32% of their gross income on household expenses. 6. A couple in Yellowknife with a combined total annual gross income of \$62,000 wish to purchase a new home. They have found the home of their dreams for \$180,000. They have saved enough to make a down payment of \$25,000. A friend has agreed to provide a 20-year mortgage at 7 1 % interest. The annual tax bill on the house is \$2,597. 4 Monthly heating costs are estimated at \$230. Find the monthly mortgage payment. Then, determine their gross debt service ratio. Do you think they should purchase this home? Why? Extension 7. In Example 1 on page 46, your gross debt service ratio was 31.7%. Explain why it may be an unwise decision to purchase this condo at this time.
• 54 Essentials of Mathematics 12 Exploration 5 Property Insurance Imagine going home today and finding your home had burned down and all of your belongings were destroyed. If you had no insurance, you would be left with nothing. With the right insurance coverage, you would receive some money to replace your possessions. Property insurance provides coverage in the event of your property being damaged or destroyed by flooding, earthquake, vandalism, or fire. Some companies will sell you “market value” policies, where they give you the present value of the item in the event of a loss. Used cars are the most likely items to be covered by market value insurance. Insurance companies also sell “replacement value” insurance, where no matter the age or condition of the loss, the company agrees to replace it with new items. Tenant’s Package Policies Most insurance companies have a “basic” or standard form of insurance, as well as a “comprehensive” form. For our purposes, all policies will have a \$500 deductible, meaning the policy-holder would be responsible for paying the first \$500 of the loss. You are able to purchase a \$200 deductible policy by adding 10% to the cost of the policy. People renting apartments or houses do not have to insure the property. However, they may wish to buy insurance for the contents. This is usually called a Tenant’s Package Policy. Goals New Terms In this exploration, you will investigate market value: the age and property insurance and select a policy to deterioration of the items are reflected in meet your needs. the appraisal. replacement value: with reference to insurance policies, it means stolen or damaged items are replaced with new items. Tenant’s Package Policy: insurance policy that protects renters from loss of contents of their rental units or personal belongings.
• Chapter 1 Personal Finance 55 Table 5 Tenant’s Package Policy (\$500 deductible) All Areas Coverage Amount Standard Form Comprehensive Form \$25,000 \$158.00 \$200.00 \$30,000 \$174.00 \$226.00 \$35,000 \$199.00 \$252.00 \$40,000 \$212.00 \$269.00 \$45,000 \$235.00 \$298.00 \$50,000 \$254.00 \$324.00 \$55,000 \$272.00 \$346.00 \$60,000 \$293.00 \$373.00 \$65,000 \$315.00 \$400.00 \$70,000 \$337.00 \$427.00 \$75,000 \$359.00 \$454.00 Each additional \$1,000 \$4.50 \$5.50 \$200 deductible: increase premium by 10% Items such as an expensive TV can be insured by a Tenant’s Package Policy.
• 56 Essentials of Mathematics 12 Example 1 Brian Jones rents an apartment. He calculates that the value of his clothes, stereo equipment, furniture, and other possessions is \$25,000. He wants to buy a Tenant’s Package Policy with a \$200 deductible to protect him against financial loss in the event of a robbery. He chooses the comprehensive plan. Find his annual premium. Solution Refer to the Tenant’s Package Policy table and find coverage for \$25,000. Since he chooses the comprehensive form, slide over to the third column and find the value \$200.00. Since Brian wants a \$200 deductible, add 10% of this amount to the cost: \$200 0.10 \$20.00 \$200 \$20 \$220.00 Brian’s annual premium will be \$220.00 Homeowner’s Insurance Home insurance for property owners is intended to protect in case of a loss due to theft, fire, flooding, hail damage, and other destructive events. Most mortgage companies require that any property they have financed be adequately insured. You only insure the building and its contents, since the land does not disappear in a fire. Some companies offer discounts if you have smoke detectors installed, or if the building is made of concrete. Property insurance is only in the amount it would cost to rebuild the building and replace the contents. Most companies offer both “broad” and “comprehensive” coverage. Comprehensive policies give you additional coverage for damages caused by such things as sewer back-up or vandalism. New Terms metro: with reference to homeowner’s semi-protected: with reference to insurance, this means a location within homeowner’s insurance, this means a city limits. location within 8 km of a firehall. protected: with reference to unprotected: with reference to homeowner’s insurance, this means a homeowner’s insurance, this means a location within 300 metres of a fire location more than 8 km from a firehall. hydrant.
• Chapter 1 Personal Finance 57 Table 6 Homeowner’s Annual Rate (\$500 Deductible) Home Metro Protected Semi-protected Unprotected Evaluator Broad Comprehensive Broad Comprehensive Broad Comprehensive Broad Comprehensive 80,000 355 406 236 270 320 366 405 463 85,000 376 430 251 287 340 389 427 488 90,000 397 454 260 297 352 403 452 518 95,000 418 479 272 311 368 422 478 548 100,000 438 502 299 342 405 463 504 578 105,000 462 529 314 359 425 487 535 613 110,000 486 557 325 373 441 505 565 647 115,000 510 584 340 390 461 528 599 686 120,000 534 612 364 417 494 565 632 723 125,000 558 639 379 434 514 589 669 765 130,000 571 654 388 444 526 602 705 807 135,000 595 681 406 465 550 630 744 852 140,000 612 700 418 479 567 649 782 895 145,000 636 728 433 496 587 672 825 944 150,000 659 754 448 513 607 695 867 993 155,000 682 781 463 530 627 718 911 1043 160,000 705 808 481 550 652 746 979 1121 165,000 721 825 493 564 668 765 1029 1178 170,000 743 851 508 581 688 788 1104 1264 175,000 767 878 523 598 708 811 1157 1325 180,000 790 904 537 615 729 834 1210 1386 185,000 812 930 555 636 753 862 1267 1450 190,000 835 956 570 653 773 885 1323 1515 195,000 860 985 588 674 797 913 1352 1548 200,000 886 1014 603 691 818 936 1381 1581 205,000 905 1035 617 707 836 956 1428 1635 210,000 924 1056 631 723 854 976 1475 1689 215,000 943 1077 645 739 872 996 1522 1743 220,000 962 1098 659 755 890 1016 1569 1797 19* 21 14 16 18 20 47 54 *charges for each additional \$5,000 increase \$200 Deductible: add 10% Solid fuel burning appliance: add 25% Age of Dwelling Discounts Discount Other Discounts Discount New home — less than 5 years old 15% mortgage free 10% 6–10 years old 10% non-smokers 5% burglar alarm 10%
• 58 Essentials of Mathematics 12 The following examples assume that all policies have a \$500 deductible. For a \$200 deductible, the policy is increased by 10%. The instructions to find the premiums over and above the listed amounts are found at the bottom of the table. Example 2 John and Rishma Sunga bought a house in a Metro area and wish to insure it. They calculate that the house and its contents are worth \$125,000. They would like a \$200 deductible limit on their comprehensive policy. Calculate their annual premiums. Solution Refer to the Homeowner’s Annual Rate table. Metro is within city limits. The comprehensive rate for \$125,000 is \$639.00. To get the \$200 deductible, add 10% to the premium: \$639 (\$639 0.10) \$702.90 Project Activity Assume you are purchasing a home worth \$150,000. Find the rates of three companies that insure property, and select one of these companies to be your insurance provider. Justify why you selected the standard or the comprehensive policy and a given deductible level. Calculate your annual property insurance premium. Be sure to include where you found the rates. Mental Math Determine the annual property insurance premiums: a) \$80,000 at \$5.00 per \$1,000 b) \$100,000 at \$6.50 per \$1,000 c) \$200,000 at \$4.50 per \$1,000
• Chapter 1 Personal Finance 59 Notebook Assignment To complete this assignment, use Table 5 on page 55 and Table 6 on page 57. 1. Ian Harding is renting an apartment. His possessions are worth \$60,000. He wants a Tenant’s Package Policy with a \$500 deductible. Find his annual premium. 2. Sam Smith’s house is located 8 kilometres from the nearest firehall. The building is worth \$165,000. He wants to purchase a comprehensive policy with a \$200 deductible. Find his annual premium. 3. Henrietta Dumont has built her dream home just outside the city, but within 300 metres of a fire hydrant. The home is worth \$210,000. She would like to get broad coverage, but with a \$200 deductible. Find her annual premium. 4. A property is insured for \$100,000 with a \$200 deductible. A fire damages the the roof and collapses the garage. It will cost about \$75,000 to repair the damage. How much money can the owner expect to receive from the insurer? A house that is farther from a firehall will have higher insurance premiums.
• 60 Essentials of Mathematics 12 5. Catherine Halliday bought a home 9 kilometres from town. She wants to insure the property and her belongings. The home is worth \$140,000. Catherine would like to have broad coverage with a \$500 deductible. Find her annual premium. 6. A property is purchased for \$180,000, including the building and the land. Explain why the insurance company will only insure the property for \$125,000. Extension 7. Rosie Miller visits the local insurance office to update her policies. She is a 25-year-old non-smoker. Rosie just bought a home in Maple Ridge worth \$210,000. If she chooses to purchase \$100,000 in whole-life insurance and comprehensive property insurance with a \$200 deductible, find her total annual insurance premiums. When you purchase house insurance, it is calculated on the value of the building separately from the value of the land.
• Chapter 1 Personal Finance 61 Exploration 6 Additional Costs in Purchasing a Home Beyond the mortgage payment, moving into a new home can be quite costly. Many one-time expenses are necessary to complete the transaction. Before a financial institution will approve a mortgage, you will need to have the property appraised to verify its value. If you have a high-ratio mortgage, then you will have to purchase insurance through the Canada Housing and Mortgage Corporation (CMHC). The municipality will demand a property survey to ensure the building is within the specified boundaries. Lawyers have to register the title to your property. Various costs such as immediate repairs, decorating, landscaping, moving, utility hook-ups, and appliances all have to be considered. They can add up to many thousands of dollars, and can even cause you to reconsider whether the time is right to buy that house. The buyers are partially responsible for some of the costs listed below, and the calculations can be tricky. For example, if you move into a home on April 1, then you are not responsible for the whole year’s property taxes, just 9 out of 12 months, or 75% of them. Goals In this exploration, you will investigate additional costs associated with buying a home and prepare a budget that itemizes them.
• 62 Essentials of Mathematics 12 Additional Costs in Purchasing a Home Item Amount Appraisal Fee Inspection Fee Property Survey Insurance for a High Ratio Mortgage Home Insurance Land Transfer Tax Prepaid Property Taxes and Utilities E MPL Legal Fees and Disbursements Sales Tax SA Moving Expenses Service Charges Immediate Repairs Appliances Decorating Costs Total Additional Costs Example 1 The Baileys live in Dauphin, MB, and are relocating to Winnipeg. They purchase a house for \$120,000 and hire a mover to move their personal belongings. The mover charges \$1,500 plus GST. They hire a lawyer to look after the legalities for a fee of \$800 plus GST. An appraisal of the property is done at a cost of \$120 plus GST. A survey of the property is done for a cost of \$450 plus GST. The Baileys’ possession date is July 7th, 2003. The interest adjustment is \$440. Annual property taxes are \$1,750, for which the Baileys will pay for the six months of July to December. Before moving in, the Baileys have sod installed in the yard for \$1,500 plus PST and GST, and they replace the stove and refrigerator for \$750 and \$900, respectively. Both appliances have PST and GST added to the cost. They split the costs of the appliances with the seller. Mrs. Bailey replaces the drapes in the living room for \$500 plus PST and GST and has the master bedroom and kitchen painted for \$350 plus GST.
• Chapter 1 Personal Finance 63 The Baileys need to increase their homeowner’s insurance. They decide to upgrade their existing policy and apply it to their new home for the remaining four months of the policy year. The old annual premium was \$264 and the new annual premium is \$680. It costs \$65 plus GST to hook up a telephone and to activate the natural gas costs \$45 plus GST. PST for Manitoba is 7%. Find the total additional costs the Baileys must pay. Solution Item Cost Tax Total mover \$1,500.00 \$1,500.00 0.07 \$105.00 \$1,605.00 lawyer \$800.00 \$800.00 0.07 \$56.00 \$856.00 appraisal \$120.00 \$120.00 0.07 \$8.40 \$128.00 survey \$450.00 \$450.00 0.07 \$31.50 \$481.50 interest adjustment \$440.00 0 \$440.00 taxes (\$1,750.00 0.5) \$875.00 0 \$875.00 sod \$1,500.00 \$1,500 0.14 \$210.10 \$1,710.00 appliances [(750 + 900) ÷ 2] \$825.00 \$825.00 0.14 \$115.50 \$940.50 drapes \$500.00 \$500.00 0.14 \$70.00 \$570.00 painting \$350.00 \$350.00 0.07 \$24.50 \$374.50 4 insurance [(680 264) ——] 12 \$138.67 0 \$138.67 utility hook-up \$110.00 \$110.00 0.07 \$7.70 \$117.70 Subtotal \$7,608.67 \$628.70 \$8,237.37 The total additional costs are \$7,608.67 + \$628.70 \$8,237.37