After visiting several automobile dealerships, Richard selects the car he wants. He likes its $11,000 price, but financing through the dealer is no bargain. He has $2,200 cash for a down payment, so he needs an $8,800 loan. In shopping at several banks for an installment loan, he learns that interest on most automobile loans is quoted at add-on rates. That is, during the life of the loan, interest is paid on the full amount borrowed even though a portion of the principal has been paid back. Richard borrows $8,800 for a period of four years at an add-on interest rate of 8 percent.
What is the annual percentage rate (APR)? (Enter your answer as a percent rounded to 2 decimal places.)
8.33%
To find the annual percentage rate (APR) for the loan, we need to calculate the total interest paid over the four-year period.
First, let's calculate the interest paid per year. Since it's an add-on interest rate, the interest is paid on the full amount borrowed throughout the loan term.
Interest per year = Loan amount * Interest rate
Interest per year = $8,800 * 0.08
Interest per year = $704
Next, we find the total interest paid over the four-year period.
Total interest paid = Interest per year * Number of years
Total interest paid = $704 * 4
Total interest paid = $2,816
Now, let's calculate the total amount repaid over the four-year period.
Total amount repaid = Loan amount + Total interest paid
Total amount repaid = $8,800 + $2,816
Total amount repaid = $11,616
Finally, we can calculate the APR using the formula:
APR = (Total interest paid / Loan amount) * (100 / Number of years)
APR = ($2,816 / $8,800) * (100 / 4)
APR = 0.32 * 25
APR = 8
Therefore, the annual percentage rate (APR) for the loan is 8 percent.
To find the Annual Percentage Rate (APR) of the loan, we need to convert the add-on interest rate to the equivalent APR.
First, let's calculate the interest amount Richard will pay over the life of the loan.
Interest = Loan Amount * Interest Rate
= $8,800 * 8%
= $704
Next, let's calculate the total amount Richard will repay over the course of the loan, including the interest.
Total Repayment Amount = Loan Amount + Interest
= $8,800 + $704
= $9,504
Now, we can calculate the APR using the formula:
APR = (Total Interest / Loan Amount) * (12 / Number of Months) * 100
APR = ($704 / $8,800) * (12 / 48) * 100
= (0.08) * (0.25) * 100
= 2
Therefore, the Annual Percentage Rate (APR) for the loan is 2%.