To purchase a used automobile, you borrow $10,000 from Loan Shark Enterprises. They tell you the interest rate is 1% per month for 35 months. They also charge you $200 for a credit investigation, so you leave with $9,800 in your pocket. The monthly payment they calculated for you is $385.71/month. If you agree to these terms and sign their contract, what is the actual APR (annual percentage rate) that you are paying?

The actual APR (annual percentage rate) that you are paying is 12.69%.

Explanation:

The actual annual percentage rate (APR) can be calculated using the Annual Percentage Rate (APR) formula as

follows:

APR = (((Fees + Interest accrued) / Principal / n) * Number of months in a year) * 100 ……………… (1)

Where;

APR = ?

Fees = Credit investigation charged = $200

Principal = Amount borrowed = $10,000

Total accrued amount = Principal * (1 + (Monthly interest rate * Number of months of loan tenure)) = $10,000 * (1 + (1% * 35)) = $13,500

Interest accrued = Total accrued amount - Principal = $13,500 - $10,000 =$3,500

n = Number of months of loan term = 35

Number of months in a year = 12

Substituting the values into equation (1), we have:

APR = (((200 + 3500) / 10000 / 35) * 12) * 100

APR = 12.69%

Therefore, the actual APR (annual percentage rate) that you are paying is 12.69%.

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