Anna wants to have $5,000 saved when she graduates from college so that she will have...

Anna wants to have $5,000 saved when she graduates from college so that she will have a down payment for a new car. She already saved $300 dollars and her credit union pays 4% annual interest compounded monthly. How much money should she deposit each month to have the money available when she graduates in 3 years?

Expert Solution

Step 1) Calculate the future value of the existing $300 after 3 year:

We are given the following information

Value of account at time 0	PV	$ 300.00
rate of interest	r	4.00%
number of years	n	3
Monthly Compounding	frequency	12
Future value	FV	To be calculated

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

So the FV is $338.18

Step 2) Subtract the above calcualted FV from the required 5000 to calculate the balancing FV required to be accumulated from the monthly payments:

5000 - 338.18 = 4661.82

Step 3) Calculate the payment required to achieve the balancing FV:

We are given the following information:

Monthly payment	PMT	To be calculated
rate of interest	r	5.00%
number of years	n	3
Annual Compounding	T	12
Balancing Future value	FV	$ 4,661.82

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

So she needs to save 120.29 monthly

Rahul Sunny answered 8 months ago

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