Question

An investment offers $10,000 at the end of each year for ten
years.

a. | If you can earn 10 percent annually, what is this investment worth today? |

b. |
If you do not spend the annual payment but invest it at 10 percent, how much will you have after the ten years have lapsed? |

Answer #1

Answer a.

Annual Payment = $10,000

Annual Interest Rate = 10%

Period = 10 years

Present Value = $10,000/1.10 + $10,000/1.10^2 + $10,000/1.10^3 +
.... + $10,000/1.10^10

Present Value = $10,000 * (1 - (1/1.10)^10) / 0.10

Present Value = $10,000 * 6.14457

Present Value = $61,445.70

So, value of this investment is $61,445.70

Answer b.

Future Value = $10,000*1.10^9 + $10,000*1.10^8 + $10,000*1.10^7
+ ... + $10,000

Future Value = $10,000 * (1.10^10 - 1) / 0.10

Future Value = $10,000 * 15.93742

Future Value = $159,374.20

So, balance after 10 years is $159,374.20

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