Yesterday, Mars Inc. borrowed $225,000 from its bank at a simple interest rate of 12 percent. The loan is for nine months and the loan agreement requires the interest to be added to the amount borrowed and the total amount to be repaid in monthly installments. What is the loan's approximate annual percentage rate (APR).

Question

Yesterday, Mars Inc. borrowed $225,000 from its bank at a simple interest rate of 12 percent. The loan is for nine months and the loan agreement requires the interest to be added to the amount borrowed and the total amount to be repaid in monthly installments. What is the loan's approximate annual percentage rate (APR).

Quizplus · Accepted Answer

The APR can be calculated by first finding the total interest paid over the 9 months, then annualizing that interest to find the equivalent yearly rate. The interest for 9 months on $225,000 at 12% simple interest is: Interest = Principal × Rate × Time = $225,000 × 0.12 × (9/12) = $20,250. The total amount to be repaid is $225,000 + $20,250 = $245,250. Since this is repaid in monthly installments over 9 months, each installment is $245,250 / 9 = $27,250. To find the APR, we need to compare this to the original loan amount and adjust for a full year. The interest component over 9 months is $20,250, which annualizes to $20,250 / 9 × 12 = $27,000. The APR is then ($27,000 / $225,000) × 100% = 12% × (12/9) = 16% × 1.35 = 21.60%.