Question

Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 70.00. 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 70.0 when he fully retires, he will begin to make annual withdrawals of $182,480.00 from his retirement account until he turns 92.00. 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 8.00% interest rate.

Answer 1

Calculation of Amount at the age of 70:

Rate = 8%

Nper = 92 - 70 = 22

PMT = 182480

FV = 0

Amount at the age of 70 can be calcculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(8%,22,-182480,0)
= $1,861,431.70

Calculation of amount at the age of 65:

Rate = 8%

Nper = 70 - 65 = 5

FV = 1861431.70

PMT = 0

Amount at the age of 65 can be calcculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(8%,5,0,-1861431.70)
= $1,266,859.14

Calculation of annual contribution:

Rate = 8%

Nper = 40

FV = 1266859.14

PV = 0

Annual contribution can be calculated by using the following excel formula:
=PMT(rate,nper,pv,fv)
=PMT(8%,40,0,-1266859.14)
= $4,890.28

Contribution = $4,890.28