Question

You have turned 35 years old and have recently switched to a new job. You have $70,000 in the retirement plan from your former employer. You will roll that money into the retirement plan of the new employer. In addition, you will contribute $8,000 each year into your new employer’s plan. If the rolled-over money and the new contributions both earn an 8 percent return, how much money would you expect to have when you retire in 28 years? How much money can you afford to withdraw monthly for those 28 years?

Answer 1

Present Value of rolled amount = PV = $70000

Deposits made each year = P = $8000

Number of deposits made = n = 28

Interest Rate earned = r = 8%

Value in account after 28 years = FV = PV(1+r)ⁿ + P(1+r)^n-1 +....+ P(1+r)² + P(1+r) + P

= PV(1+r)ⁿ + P[(1+r)ⁿ -1]/r

= 70000(1+0.08)²⁸ + 8000[(1+0.08)²⁸ -1]/0.08

= $1,366,608.09

Let the amount that can be withdrawn each month be X

Present Value in account = PV = $70000

Number of withdrawals = n = 28*12 = 336

Monthly Interest Rate = r = 8%/12

Hence, PV = X/(1+r) + X/(1+r)² +....+ X/(1+r)ⁿ = X[1- (1+r)^-n]/r

=> 70000 = X[1- (1+0.08/12)^-336]/(0.08/12)

=> X = 70000*(0.08/12)/[1- (1+0.08/12)^-336]

= $522.73