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# 1 4 compound-interest

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### 1 4 compound-interest

1. 1. Compound Interest
2. 2. <ul><li>Compound interest – a type of interest which results from the periodic addition of simple interest to the principal. </li></ul><ul><li>This type of interest often applies to savings accounts, loans, and credit cards. </li></ul><ul><li>Compound amount – the amount at the end of the term (after several compounding). </li></ul><ul><li>It is the sum of the original principal and its compound interest. </li></ul>
3. 3. <ul><li>Formula for the compound amount F : </li></ul>
4. 4. <ul><li>Example. Find the compound amount at the end of 12 periods if the principal is Php25,000 and the interest per period is 10%. </li></ul>
5. 5. <ul><li>Example. What is the maturity value of a 75,000-peso, three-year investment earning 5% compounded monthly? </li></ul>
6. 6. <ul><li>Example. Find the compound amount after 5 years and 9 months if the principal is Php150,500 and the rate is 7% compounded annually. </li></ul>
7. 7. <ul><li>More Formulas: </li></ul>
8. 8. <ul><li>1. Given P = Php 25,200 , i = 3% , n = 16 , find F . </li></ul>
9. 9. <ul><li>3. Given P = Php 1.8M , j = 11% , t = 7.5 years, m = 2 , find F . </li></ul>
10. 10. <ul><li>5. Given F = Php 46,000 , j = 12% , t = 6.25 years, m = 12 , find P . </li></ul>
11. 11. <ul><li>7. Given F = Php 56,471.27 , P = Php 25,000 , t = 8 years 3 months, m = 4 , find j . </li></ul>
12. 12. <ul><li>11. Given F = Php 34,500 , P = Php 30,000 , j = 15% , m = 12 , find n . </li></ul>
13. 13. <ul><li>13. Given F = Php 72,157.25 , P = Php 48,200 , j = 9% , m = 12 , find n . </li></ul>
14. 14. <ul><li>23. Find the compound amount due in 6 years and 2 months if Php350,000 is invested at 12% compounded monthly. </li></ul>
15. 15. <ul><li>27. How much must Ella deposit in a bank that pays 11% compounded quarterly so that she will have Php400,000 after 4 years? </li></ul>
16. 16. <ul><li>28. A personal computer was bought on installments – Php5,000 downpayment and the balance of Php22,000 in 2 years. What is the cash price if the interest rate is 20% compounded quarterly? </li></ul>
17. 17. <ul><li>30. On April 15, 2011, Justin borrowed Php1.4M. He agreed to pay the principal and the interest at 8% compounded semi-annually on July 15, 2016. How much will he pay then? </li></ul>
18. 18. <ul><li>33. At what rate converted quarterly will Php30,000 become Php40,000 in 7 years? </li></ul>
19. 19. <ul><li>37. If Php80,000 is invested at the rate of 6 ½% compounded annually, when will it earn interest of Php15,000? </li></ul>
20. 20. <ul><li>Equation of values – a mathematical statement which says that the dated values of two sets of amounts are equal when brought to a particular point in time (the comparison date). </li></ul><ul><li>In the context of borrowing, the equation of values says that </li></ul><ul><li>obligations = payments </li></ul><ul><li>These sums are obtained by either accumulating or discounting the debts incurred or the payments made toward the comparison date. </li></ul>
21. 21. <ul><li>45. What single payment at the end of 6 years would replace the following debts? </li></ul><ul><li>a) Php29,000 due in 1 year without interest </li></ul><ul><li>b) Php690,000 due in 8 years at 14% compounded quarterly </li></ul><ul><li>Money is worth 8.5% effective. </li></ul>Obligation(s) Payment(s) 1 6 8
22. 22. Obligation(s) Payment(s) 1 6 8
23. 23. <ul><li>47. For an amount borrowed from a credit cooperative, Janice needs to pay Php100,000 in 5 years. After 2 ½ years , she made a Php50,000 payment. If money is worth 8% compounded semi-annually, how much would she have to pay on the 5th year to fully settle the loan? </li></ul>Obligation(s) Payment(s) 2.5 5
24. 24. Obligation(s) Payment(s) 2.5 5
25. 25. <ul><li>49. If money is worth 8% effective, what single payment in 5 years will repay the following two debts: </li></ul><ul><li>a) Php125,000 due at once </li></ul><ul><li>b) Php500,000 due in 8 years </li></ul>Obligation(s) Payment(s) 1 5 8
26. 26. Obligation(s) Payment(s) 1 5 8
27. 27. <ul><li>51. As payments for debts of Php300,000 due at the end of 4 years and Php485,000 at the end of 8 years, Jane agrees to pay Php50,000 at once and Php250,000 at the end of 5 years. She will make a third and final payment at the end of 10 years. How much would it be if money is worth 14% compounded semi-annually. </li></ul>Obligation(s) Payment(s) 1 4 5 8 10
28. 28. Obligation(s) Payment(s) 1 4 5 8 10