Fritz benjamin buys a car costing $12300. He agrees to make payment at the end of each month period for 8 years. He pays 7.2% interest compounded monthly. what is the amount of each payment? find the total amount of interest fritz will pay?
To find the amount of each monthly payment and the total amount of interest Fritz will pay, we can use the formula for calculating the monthly payment on a loan with compound interest.
The formula for calculating the monthly payment is:
P = (r * A) / (1 - (1 + r)^(-n))
where:
P = Monthly payment
r = Monthly interest rate (in decimal form)
A = Loan amount
n = Number of monthly payments
Let's calculate the amount of each payment first:
Loan amount (A) = $12,300
Number of monthly payments (n) = 8 years * 12 months/year = 96 months
Monthly interest rate (r) = 7.2% / 100% / 12 months = 0.006
Plugging these values into the formula, we can calculate the monthly payment (P):
P = (0.006 * 12,300) / (1 - (1 + 0.006)^(-96))
Now, let's calculate the total amount of interest paid over the 8-year period:
Total interest paid = (P * n) - A
Substituting the calculated monthly payment (P) and the number of monthly payments (n) into the formula, we can find the total interest paid.
Now, let me calculate the monthly payment and the total interest for you.
12300*7.2=885.6
7.2%*8=57.6