Question

Thomas is not too bright. He wants to have $5,000 saved up in 6 years so that he can surprise his parents with a luxurious vacation for their 50th wedding anniversary. If he invests $1,000 today as a lump sum in a bank account that compounds interest quarterly, what annual interest rate will he need in order to achieve his goal?

Answer 1

Answer:

31%

Explanation:

The equation that describes the future value of a lump sum (A) invested for 'n' years at an annual rate 'r' compounded quarterly is:

$FV = A*(1+\frac{r}{4})^{4n}$

If Thomas invested $1,000 for 6 years and wants $5,000, the interest rate must be:

$6,000 = 1,000*(1+\frac{r}{4})^{4*6}\\6 = (1+\frac{r}{4})^{24}\\r=4*(\sqrt[24]{6}-1)\\r=0.31 = 31\%$

He needs a 31% interest rate.