Question

Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 72.00. 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 72.0 when he fully retires, he will begin to make annual withdrawals of $170,683.00 from his retirement account until he turns 92.00. After this final withdrawal, he wants $1.84 million remaining in his 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 9.00% interest rate. ( round to 2 decimal places).

Answer 1

year starts at 26 years of Derek

92-26 = 66 years

Derek wants Fv = 1840000

Preset value of 1840000 for 66 years = 6232.60

Draws 170683 for 19 years from 73 to 92

PV(170683) for 19 years from 73 to 92 = 29578.29

total present value required = 6232.60+29578.29= 35810.89

contribution periodically = 3233.93 yearly

Future Value: $10,572,151.93

PV (Present Value)	$35,810.84
N (Number of Periods)	66.000
I/Y (Interest Rate)	9.000
PMT (Periodic Deposit)	$3,233.93
Starting Amount	$0.00
Total Periodic Deposits	$213,439.38
Total Interest	$10,358,712.55 Future Value: $10,572,151.93 PV (Present Value) $35,810.84 N (Number of Periods) 66.000 I/Y (Interest Rate) 9.000 PMT (Periodic Deposit) $3,233.93 Starting Amount $0.00 Total Periodic Deposits $213,439.38 Total Interest $10,358,712.55

Finally Derek Gets = $ 1840000