Question

Sarah Wiggum would like to make a single investment and have ​$2.7 million at the time of her retirement in 25 years. She has found a mutual fund that will earn 6 percent annually. How much will Sarah have to invest​ today? If Sarah invests that amount and could earn a 14 percent annual​ return, how soon could she​ retire, assuming she is still going to retire when she has ​$2.7 ​million? 

Answer 1

Answer a.

Desired Sum at retirement = $2,700,000
Interest Rate = 6%
Time to Retirement = 25 years

Amount Invested * (1 + Interest Rate)^Time to Retirement = Desired Sum at retirement
Amount Invested * 1.06^25 = $2,700,000
Amount Invested * 4.291871 = $2,700,000
Amount Invested = $629,096

So, Sarah needs to invest $629,096 today in order to have $2,700,000 at retirement.

Answer b.

Desired Sum at retirement = $2,700,000
Interest Rate = 14%
Amount Invested = $629,096

Amount Invested * (1 + Interest Rate)^Time to Retirement = Desired Sum at retirement
$629,096 * 1.14^n = $2,700,000
1.14^n = 4.291873
n * ln(1.14) = ln(4.291873)
n = 11.12 years

So, Sarah can retire in 11.12 years