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