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# 2 3 sinking-funds

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### 2 3 sinking-funds

1. 1. Sinking Funds
2. 2. <ul><li>Sinking fund – a fund-accumulation scheme wherein the amount is generated by making periodic deposits </li></ul><ul><li>In amortization problems, we usually want to find the following values: </li></ul><ul><ul><li>Periodic deposit </li></ul></ul><ul><ul><li>Amount in the fund after any k th deposit </li></ul></ul><ul><ul><li>Interest earned in any period </li></ul></ul><ul><ul><li>Increase in the fund in any period </li></ul></ul>
3. 3. <ul><li>Sinking fund schedule – a table which shows how a target amount is completely attained through periodic deposits as well as interests these deposits earn in the process </li></ul><ul><li>Sinking fund method of paying off a debt – happens when the debtor pays interest periodically and pays the principal in one lump-sum payment at the end of the term from a sinking fund </li></ul>
4. 4. <ul><li>Formulas: </li></ul><ul><li>Amount in the fund after k deposits </li></ul><ul><li>Periodic deposit </li></ul>
5. 5. <ul><li>Formulas: </li></ul><ul><li>Interest earned </li></ul><ul><li>Principal repayment </li></ul><ul><li>Periodic cost (when a sinking fund is used to pay off a debt) </li></ul>
6. 6. <ul><li>1. In order to have Php800,000 in 5 years, Shane deposits an amount each year in a sinking fund earning 6% effective. Find the annual deposit and construct the sinking fund schedule. </li></ul>
7. 7. Period Beginning amount Interest earned Regular deposit Ending amount
8. 8. Period Beginning amount Interest earned Regular deposit Ending amount 1 2 3 4 5
9. 9. Period Beginning amount Interest earned Regular deposit Ending amount 1 0 0 141,917.12 141,917.12 2 3 4 5
10. 10. Period Beginning amount Interest earned Regular deposit Ending amount 1 0 0 141,917.12 141,917.12 2 141,917.12 8,515.03 141,917.12 292,349.27 3 4 5
11. 11. Period Beginning amount Interest earned Regular deposit Ending amount 1 0 0 141,917.12 141,917.12 2 141,917.12 8,515.03 141,917.12 292,349.27 3 292,349.27 17,540.96 141,917.12 451,807.35 4 5
12. 12. Period Beginning amount Interest earned Regular deposit Ending amount 1 0 0 141,917.12 141,917.12 2 141,917.12 8,515.03 141,917.12 292,349.27 3 292,349.27 17,540.96 141,917.12 451,807.35 4 451,807.35 27,108.44 141,917.12 620,832.91 5
13. 13. Period Beginning amount Interest earned Regular deposit Ending amount 1 0 0 141,917.12 141,917.12 2 141,917.12 8,515.03 141,917.12 292,349.27 3 292,349.27 17,540.96 141,917.12 451,807.35 4 451,807.35 27,108.44 141,917.12 620,832.91 5 620,832.91 37,249.97 141,917.12 800,000
14. 14. <ul><li>3. To raise money for office space expansion, a small business operator estimates that Php15M will be needed in 4 ½ years. He projects that a certain amount must be invested every 3 months in a fund which earns interest at 12% converted quarterly. </li></ul><ul><li>a) How much is the quarterly investment? </li></ul><ul><li>b) How much will be in the fund after the 3rd deposit? </li></ul><ul><li>c) How much interest is earned on the 3rd year? </li></ul>
15. 15. <ul><li>3. To raise money for office space expansion, a small business operator estimates that Php15M will be needed in 4 ½ years. He projects that a certain amount must be invested every 3 months in a fund which earns interest at 12% converted quarterly. </li></ul><ul><li>a) How much is the quarterly investment? </li></ul>
16. 16. <ul><li>3. To raise money for office space expansion, a small business operator estimates that Php15M will be needed in 4 ½ years. He projects that a certain amount must be invested every 3 months in a fund which earns interest at 12% converted quarterly. </li></ul><ul><li>b) How much will be in the fund after the 3rd deposit? </li></ul>
17. 17. <ul><li>3. To raise money for office space expansion, a small business operator estimates that Php15M will be needed in 4 ½ years. He projects that a certain amount must be invested every 3 months in a fund which earns interest at 12% converted quarterly. </li></ul><ul><li>c) How much interest is earned on the 3rd year? </li></ul>
18. 18. <ul><li>5. Caloi and Santi want to pool their money in order to have P1M in 5 years. They will place semi-annual deposits in a fund that earns 5% compounded semi-annually. How much each of these deposits should be? </li></ul>
19. 19. <ul><li>9. A Php500,000 loan at 13% interest rate payable semi-annually is to be repaid in 10 years. Find the semi-annual expense if </li></ul><ul><li>a) the loan is to be amortized every 6 months </li></ul><ul><li>b) the loan is repaid through a sinking fund earning at 15% compounded semi-annually. </li></ul><ul><li>How much does the borrower save semi-annually by choosing the cheaper method? </li></ul>
20. 20. <ul><li>9. A Php500,000 loan at 13% interest rate payable semi-annually is to be repaid in 10 years. Find the semi-annual expense if </li></ul><ul><li>a) the loan is to be amortized every 6 months. </li></ul>
21. 21. <ul><li>9. A Php500,000 loan at 13% interest rate payable semi-annually is to be repaid in 10 years. Find the semi-annual expense if </li></ul><ul><li>b) the loan is repaid through a sinking fund earning at 15% compounded semi-annually. </li></ul>
22. 22. <ul><li>11. George borrows Php80,000, with a plan to repay the whole amount in 4 years. Between now and that time, he has to make monthly interest payments at 12% compounded monthly. The Php80,000 will be repaid by making deposits each month in a sinking fund that earns 13% compounded monthly. How much is the monthly cost of the loan? </li></ul>