Question

Jennifer Creek is saving up for a new car. She wants to finance no more than $9,000 of the $21,000 estimated price in two years. She deposits $3,900 into a savings account now and will make monthly deposits for the next two years. Contributed by Gillian Nicholls, Southeast Missouri State University If the savings account pays a nominal interest rate of 8.5% per year with monthly compounding, how much must she deposit each month? $ Enter a number

Answer 1

Price of car after 2 years = $21,000

Assume finance of $9,000

Thus she needs to pay $21,000 - $9,000 = $12,000 down payment to buy the car.

$3,900 invested now at 8.5% compounding monthly will become 3900{1 + [8.5 /(100*12)]}^(12*2) = $4620

Apart from $4620, she needs $7380 which needs to be saved through monthly recurring deposits which also earns 8.5% interest compounding monthly.

Assume the monthly payment is $X. The formula to calculate future value of monthly payments is:

12x2 7380 =X 12J00) 12(/00) X= 28{:2 =->

where 8.5 / (12*100) is the monthly rate of interest while 7380 is desired amount of money after 2 years. It gives the monthly recurring deposit of $285.2