Fritz Benjamin buys a car costing 10600$. He agrees to make payments at the end of each monthly period for 8 years. He pays 4.8% interest, compounded monthly. What is the amount of each payment? Find the total amount of interest Fritz will pay.
We can start by using the formula for monthly payment on a loan:
M = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
where M is the monthly payment, P is the principal or loan amount, r is the monthly interest rate, and n is the number of payments.
In this case, P = 10600, r = 0.048/12 (since the interest rate is given as an annual percentage rate or APR), and n = 8 * 12 = 96 (since there are 12 months in a year and 8 years of payments). Plugging in these values, we get:
M = (10600 * 0.004 * (1 + 0.004)^96) / ((1 + 0.004)^96 - 1)
M = 133.22 (rounded to the nearest cent)
So Fritz will need to make monthly payments of $133.22 for 8 years in order to pay off the loan at the given interest rate. To find the total amount of interest paid, we can subtract the principal from the total payments and round to the nearest cent:
Total payments = M * n = 133.22 * 96 = $12,796.92
Total interest = Total payments - P = 12,796.92 - 10600 = $2196.92 (rounded to the nearest cent)
Therefore, Fritz will end up paying $2196.92 in interest over the life of the loan.
To determine the amount of each payment, we can use the formula for the monthly payment on a loan:
P = A * [r(1 + r)^n] / [(1 + r)^n - 1],
where P is the monthly payment, A is the loan amount, r is the monthly interest rate (annual interest rate divided by 12), and n is the total number of payments.
Fritz buys a car costing $10,600, and the interest rate is 4.8% per year compounded monthly. So, first, we need to find the monthly interest rate:
Monthly Interest Rate = Annual Interest Rate / 12
r = 0.048 / 12
r ≈ 0.004
Fritz makes monthly payments for 8 years, so the total number of payments is:
n = 8 years * 12 payments/year = 96 payments.
Now, we can use the formula to find the monthly payment:
P ≈ 10600 * [0.004(1 + 0.004)^96] / [(1 + 0.004)^96 - 1]
P ≈ 141.42
So, the amount of each monthly payment is approximately $141.42.
To find the total amount of interest Fritz will pay, we can first find the total amount paid over the 8 years:
Total Amount Paid = Monthly Payment * Total Number of Payments
Total Amount Paid = $141.42 * 96 ≈ $13,576.32
Now, we can subtract the initial cost of the car to find the total amount of interest:
Total Interest = Total Amount Paid - Initial Cost
Total Interest ≈ $13,576.32 - $10,600 ≈ $2,976.32
The total amount of interest Fritz will pay is approximately $2,976.32.