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

r = 11.5%

Step-by-step 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 =( A)/((1 + r)^n)`

where

A - amount after given n year

`PV = (5000)/((1 + r)^5) + (50000)/((1 + r)^(10))`

`20,000 =  (5000)/((1 + r)^5) + (50000)/((1 + r)^(10))`

Let
`(1 + r)^5 = t`

squaring on both side

`(1 + r)^(10) = t^2`

`20,000 =  (5000)/(t) + (50000)/(t^2)`

`20 = (5)/(t) + (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\%`