Question

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 $4000 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 5% per year with monthly compounding, how much must she deposit each month?

Answer 1

Cost of the car = 26000

Financed amount = 10000

Amount needed in 2 year = 24 months = 16000

Interest rate = 5% per year = 5/12 = 0.417

Investment made = 4000 with a monthly amount A to be deposited every month for 24 months

The sum of the future value of the amount deposited today which is calculated using F/P and the future value of the monthly deposits which is calculated using F/A is equal to the required amount in 24 months = 16000

4000(F/P,0.417%,24)+A(F/A,0.417%,24) = 16000

4000(1.10494)+A(25.1869)=16000

4419.76+25.1869A=16000

25.1869A=16000-4419.76

A=11580.24/25.1869

A=459.77

A=$460