Question

Your second cousin has just turned 30 years old, has just received her master’s degree in

neurofinance and has accepted her first job. Now she must decide how much money to put into

her retirement plan. The plan works as follows: Every dollar in the plan is expected to earn 8%

per annum. She cannot make withdrawals until she retires on her sixty-fifth birthday. After that

point, she can make withdrawals as she sees fit. She plans on living to 100 years and working

until she turns 65. She estimates that to live comfortably in retirement, she will need $120,000

every year starting at the end of the first year of retirement and ending on her 100th birthday.

Assume that she will contribute the same amount to the plan at the end of every year that she

works. The amount of money she would need to contribute each year to fund her retirement is

closest to:

a) $7,475.

b) $8,116.

c) $8,207.

d) $8,817.

Answer 1

1]	Amount to be had on completion of the 65th birthday = The PV of the 35 year end withdrawals to be made from the 66th year to 100 th year, which constitute an annuity.
	The value of the annuity at t35 = 120000*(1.08^35-1)/(0.08*1.08^35) =	$      13,98,548
2]	The above amount is the FV of the annual payments,
	which constitue an annuity.
	Therefore, 1398548 = A*(1.08^35-1)/0.08, where A is the
	annual amount to be contributed each year end.
	Therefore, A = 1398548*0.08/(1.08^35-1) =	$               8,116
	Answer: [b] $8,116