You have arranged for a loan on your new car that will require the first payment today. The loan is for $43,500, and the monthly payments are $740.

You have arranged for a loan on your new car that will require the first payment today. The loan is for $43,500, and the monthly payments are $740.

   

Required:

If the loan will be paid off over the next 79 months, what is the APR of the loan? (Do not include the percent sign (%). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

APR

%

rev: 05-02-2011

Explanation:

Here we are given the PVA for an annuity due, number of periods, and the amount of the annuity. We need to solve for the interest rate. Using the PVA equation:

PVA = [{1 – [1 / (1 + r)]79}/ r](1 + r)

$43,500 = $740[{1 – [1 / (1 + r)]79}/ r](1 + r)

To find the interest rate, we need to solve this equation on a financial calculator, using a spreadsheet, or by trial and error. If you use trial and error, remember that increasing the interest rate decreases the PVA, and decreasing the interest rate increases the PVA. Using a spreadsheet, we find:

r = 0.0080 or 0.80%

This is the monthly interest rate. To find the APR with a monthly interest rate, we simply multiply the monthly rate by 12, so the APR is:

APR = 0.0080 × 12

APR = 0.0964 or 9.64%

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

2nd BGN  2nd SET

Enter

79

±$43,500

$740

N

I/Y

PV

PMT

FV

Solve for

0.80%

APR = 0.80%(12) = 9.64%