Question

Your parents will retire in 29 years. They currently have $200,000 saved, and they think they will need $2,400,000 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

8.95%

Step-by-step explanation:

Data provided in the question:

Time, n = 29 years

Principle amount = $200,000

Future value = $2,400,000

Now,

Using the compounding formula

Future value = Principle × [ 1 + r ]ⁿ

here,

r is the interest rate

Thus,

$2,400,000 = $200,000 × [ 1 + r ]²⁹

or

[ 1 + r ]²⁹ = 12

taking the natural log both the sides, we have

29 × ln(1 + r) = ln(12)

or

ln(1 + r) = 0.08569

or

1 + r =
`e^(0.08569)`

or

1 + r = 1.0895

or

r = 0.0895

or

r = 0.0895 × 100% = 8.95%