Calculating the APR of a Car Loan

You have arranged for a loan on your new car that will require the first payment today. The loan is for $24,500, and the monthly payments are $465. If the loan will be paid off over the next 60 months, what is the APR of the loan?

Answer:

84%

Explanation:

APR is the annual rate of interest that is paid on an investment, without taking into account the compounding of interest within that year. APR is calculated by multiplying the periodic interest rate by the number of periods in a year in which the periodic rate is applied.

Divide the finance charge by the loan amount. In this case, $3,400 divided by $24,500 equals 0.138

Multiply the result by 365 to get 50.4

Divide the result by the term of the loan. In this case, 50.4 divided by 60 is 0.84

Multiply the result by 100 to turn the answer into a percentage 84%

Final answer:

Calculating the APR of a loan from the amount borrowed, monthly payment, and term requires iterative methods or financial software because there's no simple algebraic formula.

Explanation:

To determine the APR (Annual Percentage Rate) of the loan, we need to use the formula for the present value of an annuity because the car payments are made in regular installments. The loan amount (present value) is $24,500, the monthly payment is $465, and the loan term is 60 months. Unfortunately, finding the APR requires either the use of a financial calculator, a specific APR formula, or an iterative method such as a bisection method or using spreadsheets or other financial software as there's no straightforward algebraic solution to this type of problem. Calculating APR is a typical question in financial mathematics, where the goal is to find the interest rate that equates the present value of payments to the amount borrowed.