Question

A woman wants to borrow $12,000 in order to buy a car. She wants to repay the loan by monthly installments for 4 years. If the interest rate on this loan is 10 1/2 % per year, compounded monthly, what is the amount of each payment?

Answer 1

To find the monthly payment, use the formula for an installment loan with the given details: principal of $12,000, monthly interest rate derived from the annual rate of 10.5%, and a total of 48 payments for the 4-year term.

Step-by-step explanation:

To determine the monthly payment on a $12,000 loan for a car with a 10.5% annual interest rate compounded monthly, over a period of 4 years, we can use the formula for the monthly payment (PMT) on an installment loan:

PMT = P * (i / (1 - (1 + i)^(-n)))

Where:

• P is the principal amount ($12,000)
• i is the monthly interest rate (10.5% per year / 12 months = 0.875% per month)
• n is the total number of payments (4 years * 12 months/year = 48 payments)

First, convert the annual interest rate to a monthly rate:

i = 10.5% / 12

i = 0.0875

Now calculate the monthly rate in decimal:

i = 0.0875 / 100

i = 0.000875

Next, substitute the values into the formula:

PMT = 12000 * (0.000875 / (1 - (1 + 0.000875)^(-48)))

Calculating this gives us the monthly payment amount. This formula accounts for the compounding interest and gives a fixed monthly payment for the term of the loan.