Question

An investment will pay $5,000 per year for 10 years, with the first payment occurring one year from today.

A. If the interest rate is 6%, what is the value of this investment today?

B. What would the value of the investment be if the $5,000 annual cash flow lasts 20 years (and the interest rate is still 6%)?

C. How come the value of the investment IS NOT twice as much in part B as compared to part A? (After all, you will receive double the amount of cash over the 20 year annuity: 5000 X 20 vs. 5000 X 10).

**To receive credit, you must show your work!***

Answer 1

A). Value of investment today = Annual Amount * [{1 - (1 + r)^-n} / r]

= $5,000 * [{1 - (1 + 0.06)^-10} / 0.06]

= $5,000 * [0.4416 / 0.06]

= $5,000 * 7.3601 = $36,800.44

B). Value of investment today = Annual Amount * [{1 - (1 + r)^-n} / r]

= $5,000 * [{1 - (1 + 0.06)^-20} / 0.06]

= $5,000 * [0.6882 / 0.06]

= $5,000 * 11.4699 = $57,349.61

C). It is because of power of discounting. Discounting is the process of converting the future amount into its Present Value.