Question

You decide to save for retirement with a company that offers 6.3% compounded annually. You have decided to make $5,000 yearly deposits into the account for the next 30 years. Then for the 35 years following your final deposit, you plan on taking out an equal amount of money at the end of every year. (a) How much will you be able to withdraw each year for the 35 years after your last deposit? (b) How much total interest is earned during this entire 65-year process?

Answer 1

Yearly deposit	$          5,000.00
Rate of return	6.30%
Number of deposits	30
The amount at the end of 30 years	$      416,801.37
No of withdrawals	35
Amount of withdrawal	$        29,766.52
Total amount deposited	$      150,000.00
Total withdrawn	$ 1,041,828.21
Total interest earned	$      891,828.21

Excel formulas:

.

If you want to do it without using excel refer the following:

Step 1: Find the total amount at the end of 30 years of deposit. We can use the future value of the annuity formula:

Where,
FVA = Future Value of Annuity
A = Annuity of deposits
i = rate of return
n = number of years

Therefore,

Step 2: Find the amount of withdrawal using the present value of the annuity formula:

Where,
PVA = Present value of the annuity
P = Amount of withdrawal
i = rate of return
n = Number of years

Therefore,

Step 3: Find the difference between the total amount deposited and the total amount withdrawn, that difference will the total interest earned.

Total amount deposited = 5000 * 30 =  $150,000.00

Total amount withdrawn =  $29,766.52 * 35 =  $1,041,828.21

Interest earned =  $1,041,828.21 - $150,000.00

=  $891,828.21