Question

#1

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 begin to make annual withdrawals of $131,085.00 from his retirement account until he turns 86.00. 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 10.00% interest rate.

Answer format: Currency: Round to: 2 decimal places.

Answer 1

First use,PV function in EXCEL to find the amount accumulated at 71 years.

=PV(rate,nper,pmt,fv,type)

rate=10%

nper=15 years (72-86 years)

pmt=131085

fv=0

=PV(10%,15,131085,0,0)=$997,042.93

But by another 6 years the fund should discounted to 65 years ( from 71 years) because there has been no deposits.

Fund accumulated at 65 age=$997,042.93/(1+10%)^6=$562,804.74

==> Now use PMT funcction to find the annual deposits made.

=PMT(rate,nper,pv,fv,type)

rate=10%

nper=40 years (26-65 years)

pv=0

fv=562804.74

=PMT(10%,40,0,562804.74,0)=$2252.73

Annual deposits need to made=$2252.73