Question

You will deposit $9000 into an account with an annual interest rate of 7% compounded monthly, leave the account untouched for 18 years, and then withdraw equal amounts at the end of each month for the following 9 years, ending with a balance of $9000. What will your monthly withdrawals be?

Answer 1

First we need to find the FV of the initial deposit after 18 years:

We are given the following information:

Initial deposit	PV	$              9,000.00
Rate of interest	r	7.00%
Number of years	n	18
Future value	FV	To be calculated

We need to solve the following equation to arrive at the required FV

So the FV is $30419.40

Next we calcualte the PV of the 9000 remaining balance required at the end of 9 years

We are given the following information:

Present value	PV	To be calcualted
Rate of interest	r	7.00%
Number of years	n	9
Future value	FV	9000

We need to solve the following equation to arrive at the required PV

Next we subtrac this from the FV calculated:  $30,419.4 -4895.40 =  $25,524

Using this we can calculate the annuity payments for the 9 years:

We are given the following information:

Annual payment	PMT	To be calculated
Rate of interest	r	7.00%
Number of years	n	9
Present value	PV	$            25,524.00

We need to solve the following equation to arrive at the required PMT

So the annual payments can be 3917.60