You have a twin brother who didn’t go to college and started working when he was

Question

You have a twin brother who didn’t go to college and started working when he was 18 years old. You just graduated from college and started working at the age of 23. You brother currently has $50,000 savings in his retirement account that pays 7% interest. You currently have no savings but until the next year you’ll have $15’000 savings in your retirement account. How much should be the interest rate on your retirement account so that you and your brother will retire with the same amount of savings at the age of 60?

Explanation / Answer

Solution:

Future value of savings on my account = $15,000 (FVIFA @ I, 60 - 24)

Future value of savings on my account = $15,000 (FVIFA @ I, 36)

Future value of saving on brother's account = $50,000 (FVIFA @ 7%, 60 - 18)

Future value of saving on brother's account = $50,000 (FVIFA @ 7%,42)

Future value of saving on brother's account = $50,000 [(1.07^42-1)/0.07]

Future value of saving on brother's account = $50,000 (230.63)

Future value of saving on brother's account = $11,531,612

Therefore, both will have same savings at the age of 60

11,531,612 = $15,000 (FVIFA @ I, 36)

768.77 = FVIFA @ I, 36

Solving for I, we get

I = 13.88%

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