# Your grandfather has offered you a choice of one of the following alternatives: $7500 now,$2200...

## Question:

Your grandfather has offered you a choice of one of the following alternatives: $7500 now,$2,200 a year after for nine years; or \$31,000 at the end of nine years. Assuming you could earn 10%annually, which alternative would you choose?

If you earn 11% annually would still choose the same alternative?

## Time Value of Money:

The time value of money argues that a dollar received tomorrow is not as valuable as the same dollar today. The difference is due to the time value of money, that is, the same nominal amount of money loses value as it is paid is later.

You should choose the alternative that has the highest present value. We can use the following formula to compute the present value of a payment {eq}F {/eq} received in {eq}T{/eq} periods from today, given periodic discount rate {eq}r{/eq}:

• {eq}\displaystyle \frac{F}{(1 + r)^T} {/eq}

If discount rate is 10%, then the present value of each alternative is:

• first alternative: {eq}7,500 + \dfrac{2,200*(1 - (1 + 10\%)^{-9})}{10\%} = 20,169.85 {/eq}
• second alternative: {eq}\dfrac{31,000}{(1 + 10\%)^9} = 13,147.02 {/eq}

You should choose the first alternative because it has a higher present value.

If discount rate is 11%, then the present value of each alternative is:

• first alternative: {eq}7,500 + \dfrac{2,200*(1 - (1 + 11\%)^{-9})}{11\%} = 19,681.50 {/eq}
• second alternative: {eq}\dfrac{31,000}{(1 + 11\%)^9} = 12,118.67 {/eq}

You should choose the first alternative because it has a higher present value.