Jennifer Creek is saving up for a new car. She wants to finance no more than $10,000 of the $26,000 estimated price in two years. She deposits $5,000 into a savings account now and will make monthly deposits for the next two years. If the savings account pays a nominal interest rate of 3% per year with monthly compounding, how much must she deposit each month?

$432.74

Explanation:

Since Jennifer wants to buy the car in the next two years and the car cost is $26000 and she wants to finance no more than $10,000, therefore she'll require ($26000 - $10000) = $16000.

In order for her to get $16000 for the next two years, she wants to deposit $5000 today and she'll make a month deposit which can be represented by A every month. The interest rate will be calculated as: 3%/12 = 0.03/12 = 0.0025 = 0.25% every month.

Therefore, the amount that she must deposit each month will be:

$5000(F/P,0.25%,24) + A(F/A, 0.25%, 24) = $16000

$5000(1.062) + A(24.703) = $16000

$5310 + 24.703A = $16000

24.703A = $16000 - $5310

24.703A = $10690

A = $10690/24.703

A = $432.74

The amount that she must deposit each month will be $432.74