Fritz Benjamin buys a car costing $8800. He agrees to make payments at the end of each monthly period for 6 years. He pays 6.0% interest, compounded monthly. What is the amount of each payment? Find the total amount of interest Fritz will pay.
6.0% /100=0.06
8800*0.06=?
0.06*6=?
To find the amount of each monthly payment, we can use the formula for calculating the monthly payment on a loan:
P = (r * PV) / (1 - (1 + r)^(-n))
where:
P = monthly payment
r = monthly interest rate (annual interest rate / 12, expressed as a decimal)
PV = present value (the cost of the car)
n = number of monthly payments
Step 1: Convert the annual interest rate to a monthly interest rate.
In this case, the annual interest rate is 6.0%. To convert it to a monthly rate, divide it by 12: r = 6.0% / 12 = 0.005.
Step 2: Calculate the number of monthly payments.
Since Fritz will make payments at the end of each monthly period for 6 years, the total number of payments is 6 years * 12 months/year = 72 monthly payments (n = 72).
Step 3: Substitute the values into the formula and solve for the monthly payment.
P = (0.005 * $8800) / (1 - (1 + 0.005)^(-72))
= ($44) / (1 - (1.005)^(-72))
≈ $136.82
Therefore, the amount of each monthly payment is approximately $136.82.
To find the total amount of interest Fritz will pay, we subtract the cost of the car from the total amount paid over the loan period.
Total amount paid = monthly payment * number of payments
= $136.82 * 72
≈ $9,856.64
Total interest paid = Total amount paid - Present value
= $9,856.64 - $8,800
≈ $1,056.64
Therefore, Fritz will pay approximately $1,056.64 in interest over the 6-year loan period.