Question

Chapter 02, Problem 139 You decide to open a retirement account at your local bank that pays 10%/year/month (10% per year compounded monthly). For the next 20 years, you will deposit $600 per month into the account, with all deposits and withdrawals occurring at month's end. On the day of the last deposit, you will retire. Your expenses during the first year of retirement will be covered by your company's retirement plan. As such, your first withdrawal from your retirement account will occur on the day exactly 12 months after the last deposit. Click here to access the TVM Factor Table Calculator x Your answer is incorrect. Try again. What monthly withdrawal can you make if you want the account to last 25 years?.. Round entry to the nearest dollar. Tolerance is ±4 Your answer is incorrect. Try again. What monthly withdrawal can you make if you want the account to last forever (with infinite withdrawals)? Round entry to the nearest dollar. Tolerance is ±4

Answer 1

Monthly deposit = $600 per month

Monthly rate = 10%/12

Time = 20*12 = 240 months

Withdrawal starts after 12 months.

1.

Future value of deposits at the time of withdrawal = (600*((1+10%/12)^240 - 1)/(10%/12))(1+10%/12)^12

Future value of deposits at the time of withdrawal = $503330.8

Let, monthly withdrawal for 25 years is P.

Time = 25*12 = 300 months

Then,

503330.8 = P*(1 - 1/(1+10%/12)^300)/(10%/12)

P = 503330.8/110.05

P = $4573.66 or $4574

So, monthly withdrawal for the 25 years will be $4573.66 or $4574.

2.

If withdrawal is for infinite period

Then,

Monthly withdrawal = 503330.8*10%/12 = 4194.42 or 4194

So, monthly withdrawal will be  $4194.42 or $4194