Question

Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 71.00. During these years of part-time work, he will neither make deposits to nor take withdrawals from his retirement account. Exactly one year after the day he turns 71.0 when he fully retires, he will wants to have $2,612,520.00 in his retirement account. He he will make contributions to his retirement account from his 26th birthday to his 65th birthday. To reach his goal, what must the contributions be? Assume a 10.00% interest rate.

Answer 1

Derek is going to contribute in retirement account till 65th birthday. Thus from 65th birthday till 71th birthday, he is going to get interest.

Value of retirement account on = $2,612,520 * PVIF(10%, 6)

                                             = $2,612,520 * [ 1/1.10 + 1/1.10² + ..... + 1/1.10⁶ ]

                                             = $2,612,520 * 0.5645

                                             = $ 1,474,767.54

From first contribution on 26th birthday till 65th birthday, future value will be $ 1,474,767.54 as on 65th birthday

Future value = Contribution * FVAF(r, n)

1474767.54 = Contribution * FVAF(10%, 39) + Contribution on 65th birthday

1474767.54 = Contribution * ( FVAF(10%, 39) + 1 )

1474767.54 = Contribution * ( 401.4478 + 1 )

1474767.54 = Contribution * 402.4478

Contribution = 1474767.54 / 402.4478

Contribution = $ 3664.50 per year Answer