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# Applied Math 40S Slides May 9, 2007 - Part 2

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Afternoon class. Two review problems and a more involved one comparing the cost/benefit of buying vrs. renting.

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### Applied Math 40S Slides May 9, 2007 - Part 2

1. 1. To my substitute: The student's assignment is in this document on the smart board. They know what to do. Tennyson will help you shut everything down after class. Students should be sitting and working in groups on these problems and collaborating to write the answers on the smart board. I will be verifying their work first thing tomorrow morning. These are wonderful students, sit back and watch them do their thing. ;-) Thanks, Darren Kuropatwa
2. 2. Ms. Johnston has decided to buy a home. She requires a \$65 000 mortgage. The mortgage interest rate is 7.75%, and she will repay the mortgage with monthly payments. She needs to decide whether she will select a 20- or 15-year amortization term. How much do her monthly payments increase, and how much money will she save if she chooses a 15-year term instead of a 20-year term? Would you advise Ms. Johnston to get a 15- or 20-year mortgage? Why?
3. 3. T. Bekka needs a \$105 000 mortgage which he will repay with monthly payments in 25 years. The first bank he visits offers a mortgage at 8.5%, and the second bank at 7.9%. (a) How much does he save each month if he takes the second offer? (b) How much does he save over the life of the mortgage if he takes the second offer?
4. 4. Rent or Buy? A Case Study ... The Browns have an opportunity to buy a home valued at \$50 000 with a down payment of \$5000 and a mortgage of \$45 000, or rent the home for \$525 per month. If they buy, they will get a 15-year mortgage at 7.5%. Annual property taxes are approximately 1.5% of the market value (i.e. the sale price) of the home. They expect their home to appreciate in value by about 2% per year. (That is, it will become 2% MORE VALUABLE each year. If it is worth \$100 this year, next year it will be worth \$102 and the year after that it would be worth \$104.04.) If they rent, their rental payments will increase by 3% each year, and they expect to get a 7% annual return on their investment of the \$5000 they did not use as a down payment. Questions on next page ...
5. 5. (a) What is the size of the monthly mortgage payment? (b) What will their equity be in the home after two years of ownership? (c) After one year, how does the cost of payments plus property taxes compare with the cost of rental payments? (d) After 10 years, how does the annual cost of payments plus property taxes compare with the annual cost of rental payments? (e) What might be some reasons for the Brown family to rent instead of buy - even though renting seems to be more expensive in the long run? (f) What is the net cost of owning the home for 10 years? Of renting for 10 years?
6. 6. The Answers ... (1) Savings are: \$126,892.80 - \$109,312.20 = \$17,580.60 Might advise Ms. Johnston to get the 15-year mortgage if she can afford an additional \$80 per month mortgage payment because over the life of the mortgage she will save over \$17,000, and be free of debts five years sooner. (2) (a) Monthly saving is \$40.45 (b) Total saving in 25 years is \$12,134.43 (3) (a) \$414.23 (b) \$8538.72 (c) Renting is more expensive by: \$6300.00 - \$5720.76 = \$579.24 (d) Renting is more expensive by: \$8220.12 - \$5885.01 = \$2335.11 (e) Possible answers: • They do not have enough money for a down payment, or decide to spend the money on something else. • They plan to stay in this home for only a short time. • They have a poor credit rating and cannot get a mortgage. (f) Net Ownership Cost: =Total Costs - Credits = \$62,919.89 - \$29,271.39 = \$33,648.50 Net Rental Cost = \$72,222.44 - \$4835.76 = \$67,386.68 Therefore, \$67,386.68 - \$33,648.50 = \$33,738.18 greater renting than owning.