Question

Ben invested $20,000 into a money market account and took out $5,000 at the end of year 5. He found out at the end of 10 years that he had as of $50,000 in the account. What is the annual interest rate Ben had earned on this investment

Answer 1

Answer:

r = 11.5%

Explanation:

Given data:

invested amount $20,000

withrawl amount after 5 year is $5000

Amount at the end of 10th yr is $50,000

present value  is given as

$PV =\frac{ A}{(1 + r)^n}$

where

A - amount after given n year

$PV = \frac{5000}{(1 + r)^5} + \frac{50000}{(1 + r)^{10}}$

$20,000 =  \frac{5000}{(1 + r)^5} + \frac{50000}{(1 + r)^{10}}$

 Let $(1 + r)^5 = t$

squaring on both side

$(1 + r)^{10} = t^2$

$20,000 =  \frac{5000}{t} + \frac{50000}{t^2}$

$20 = \frac{5}{t} + \frac{50}{t^2}$

$20 t^2 - 5t - 50 = 0$

solving for t we get

t = 1.711

so, $r = 1.711^{1/5} -1 = 0.115 = 11.5\%$