Question

Suppose a recent college graduate's first job allows her to deposit $200 at the end of each month in a savings plan that earns 9%, compounded monthly. This savings plan continues for 6 years before new obligations make it impossible to continue. If the accrued amount remains in the plan for the next 15 years without deposits or withdrawals, how much money will be in the account 21 years after the plan began? (Round your answer to the nearest cent.)

Answer 1

First we need to calculate teh FV of the payments made in the first 6 years at the end of the 6th year and then we need to compound it for 15 years to find the final future value:

To calculate the FV at the end of year 6, We are given the following information:

MOnthly deposit	PMT	$                  200.00
Rate of interest	r	9.00%
Number of years	n	6
Compounding frequency	T	12
Future value at the end of year 6	FV6	To be calculatef

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

So the FV at the end of year 6 is $19001.41

Now we need to compound it for 15 years to the end of year 21

We are given the following information:

Future value at the end of year 6	FV6	$            19,001.41
Rate of interest	r	9.00%
Number of years	n	15
Compounding frequency	frequency	12
Future value at the end of year 21	FV21	$            72,928.22

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

So the FV at the end of year 21 is $72928.22