Fritz Benjamin buys a car costing $\$ 5700$. He agrees to make payments at the end of each monthly period for 8 years. He pays $9.6 \%$ interest, compounded monthly. What is the amount of each payment? Find the total amount of interest Fritz will pay.
Fritz's monthly payment is $\$ \square$.
(Round to the nearest cent.)
Answer
Final Answer: Fritz's monthly payment is approximately \(\boxed{\$85.29}\). The total amount of interest Fritz will pay is approximately \(\boxed{\$2487.94}\).
Step 1 ：Given that Fritz Benjamin buys a car costing $5700. He agrees to make payments at the end of each monthly period for 8 years. He pays 9.6% interest, compounded monthly.
Step 2 ：We can calculate the monthly payment using the formula for the monthly payment on an amortizing loan: \(P = \frac{r \cdot PV}{1 - (1 + r)^{-n}}\), where \(P\) is the monthly payment, \(r\) is the monthly interest rate (annual interest rate divided by 12), \(PV\) is the present value or principal amount of the loan (in this case, the cost of the car), and \(n\) is the total number of payments (or periods), which is the loan term in months.
Step 3 ：Substituting the given values into the formula, we get \(P = \frac{0.008 \cdot 5700}{1 - (1 + 0.008)^{-96}}\).
Step 4 ：Solving the equation, we find that the monthly payment Fritz needs to make for his car loan is approximately $85.29.
Step 5 ：We can calculate the total amount of interest Fritz will pay by multiplying the monthly payment by the total number of payments and then subtracting the principal amount of the loan.
Step 6 ：Substituting the values into the formula, we get \(total\_interest = 85.29 \times 96 - 5700\).
Step 7 ：Solving the equation, we find that the total amount of interest Fritz will pay is approximately $2487.94.
Step 8 ：Final Answer: Fritz's monthly payment is approximately \(\boxed{\$85.29}\). The total amount of interest Fritz will pay is approximately \(\boxed{\$2487.94}\).
