Question

Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 73.00. 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 73.0 when he fully retires, he will begin to make annual withdrawals of $115,952.00 from his retirement account until he turns 95.00. 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 7.00% interest rate.

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 $151,219.00 from his retirement account until he turns 85.00. After this final withdrawal, he wants $1.10 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.

Answer 1

Answer a)

Annual Withdrawal(at end of period)	$1,15,952.0
Annual interest rate	7.0%
Number of payment(95-73)	22.0
Fund required at age of 73	$12,82,573.0	PV(7%,22,-115952,0,0)
Value of fund at age of 65 ( need to be accumulated in the retirement fund)	$7,46,469.2	1282573/(1.07^8)
Annual interest rate	7.0%
Number of payment(65-26)	39.0
Annual contribution(at start )	$3,758.0	PMT(7%,39,0,-746469.2,1)

Annual deposit of $3,758.0

Answer b)

Annual Withdrawal	$1,15,219.0
Annual interest rate	9.0%
Number of payment(85-70)	15.0
Future Value of remaining fund	$11,00,000.0
Fund required at age of 70	$12,30,736.3	PV(9%,15,-115219,-1100000,0)
Value of fund at age of 65 ( need to be accumulated in the retirement fund)	$7,99,894.1	1230736.3/(1.09^5)
Annual interest rate	9.0%
Number of payment(65-26)	39.0
Annual contribution	$2,374.4	PMT(9%,39,0,-799894.1,1)

Annual deposit of  $2,374.4