Question

PLEASE SHOW USING FINANCIAL CALCULATOR FUNCTIONS Today is your 25^th birthday (t=0). You wish to retire when you turn 55 (t=30). You currently have $5,000 in a retirement account earning 4% p.a. In order to save for retirement, you plan on depositing $7,500 into this account every year starting next year (t=1) until your retirement date (last deposit at t=30). When you retire, you plan on withdrawing an equal amount each year starting five years after you retire (first withdrawal at t=35) until you turn 75 (last withdrawal at t=50). You also plan on giving $50,000 to your grandchildren when you turn 75 (t=50). How much can you afford to withdraw each year?

Answer 1

Amount of $5,000 on 60^Th birthday = 5,000(1.04)³⁵ = $19,730.44

Value of amount of annual deposits on 55^th birthday = 7,500*[{(1+0.04)³⁰-1}/0.04]

= $420,637.03

Value on 60^th birthday = 420,637.03(1.04)⁵ = $511,769.26

Total amount on 55^th birthday = $531,499.70

Let the annual withdrawals be x

531,499.70 = x+ x*PVAF(4%, 40 periods) + 50,000*PVF(4%, 41 periods)

531,499.70 = x+ x*19.79277 + 50,000*0.208289

X = $26,327.05

Hence, annual withdrawal = $26,327.05