Question

Your parents will retire in 22 years. They currently have $370,000 saved, and they think they will need $1,500,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds? Round your answer to two decimal places.

Answer 1

Given:

Current Savings = $ 370,000

Future Amount required = $ 1,500,000

Time Period(N) = 22 Years

Future value of current savings = Current Savings * (1 + R%) ^N

Let’s assume that R is rate of required return.

$ 1,500,000 = $ 370,000 * (1+ R%) ^22

$ 1,500,000 / $ 370,000 = (1+R) ^22

4.054 = (1+R%)^22

To solve the exponential , take natural log at both side (ln)

Ln (4.054) = ln (1+R%) ^22 = 22* ln (1+R%)

1.399717 = 22 * ln (1+R%)

1.399717/22 = ln (1+R%)

0.06362 = ln (1+R%)

(1+R%) = e ^ 0.06362 = 1.0657

R% = 1.0657 -1 = 6.57%