Question

Suppose that you are 25 years old, and making retirement plans. You are starting to contribute $600 per month to your retirement account at the beginning of each month. You intend to do so until the age of sixty seven and then stop the contributions. You will retire at age 70. You receive a 7% APR compounded monthly on your account. What could you withdraw in terms of a monthly perpetuity?                                         

Group of answer choices

< $12800                                                        

> $13400

$12800-$13000

$13200-$13400

$13000-$13200

Answer 1

Deposit of money i.e. $600 every month will happen up to 67 years, which means I will be depositing $600 every month for 42 years. And this deposit happens at the beginning of a month so it is an annuity due.

The interest rate received on deposits is 7% annually.

So the future value of this deposits at end of 67 years will be calculated by using the future value formula for an annuity due:

FV = A(1+i){(1+i)^n-1}/i

where,

A = monthly deposits = 600

i = interest rate = 7%/12 = 0.583% monthly

n = number of payments = 42*12 = 504

FV = $1,368,906.604 at end of year 67

For next three years there won't be any deposit and I will get retired at age 70.

So, value of deposit must have grown 7% annually and had become = (FV at 67)*(1.07)^3 = $1,368,906.604*(1.07)^3 = $1,676,969.453

After that, I will be drawing an amount monthly till perpetuity. So using perpetuity formula which is,

PV = A/i

where PV is the present value of deposit = $1,676,969.453

A is the monthly withdrawal amount

i is the interest rate recived monthly = 7%/12 = 0.583%

A = $8,384.847

So the answer from the choice will be <$12,800