Question

You decide to open an individual retirement account (IRA) at your local bank that pays 8%/year compounded annually. At the end of each of the next 40 years, you will deposit $4,000 into the account. Three years after your last deposit, you will begin making annual withdrawals. What annual amount will you be able to withdraw if you want the withdrawals to last: a. 20 years? b. forever?

Answer 1

Answer:

a). The annual amount you will be able to withdraw=$173,796.172

b). Annual amount you will be able to withdraw forever=$21,724.5215

Explanation:

a).

Step 1

Determine the present value of the payments as follows;

Present value=Annual deposit×number of years

where;

annual deposit=$4,000

number of years=40

replacing;

Present value=(4,000×40)=$160,000

The future value=P.V(1+r)^n

where;

P.V=$160,000

r=8%=8/100=0.08

n=40 years

replacing;

F.V=160,000(1+0.08)^40

F.V=$3,475,923.439

Annual amount of withdrawal=F.V/number of years

Annual amount of withdrawal=3,475,923.439/20=$173,796.172

The annual amount you will be able to withdraw=$173,796.172

b).

The present values that will support perpetual withdrawals can be expressed as;

Present value=Annual cash flow/interest rate

Present value=173,796.172/8%

Present value=$21,724.5215