Question

This question illustrates what is known as discount interest. Imagine you are discussing a loan with a somewhat unscrupulous lender. You want to borrow $15,000 for one year. The interest rate is 12 percent. You and the lender agree that the interest on the loan will be .12 × $15,000 = $1,800. So the lender deducts this interest amount from the loan up front and gives you $13,200. In this case, we say that the discount is $1,800. What is the effective annual rate? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

The effective annual rate of a loan taken out with discount interest, where interest is deducted from the loan amount upfront, is calculated by dividing the interest by the actual loan amount received. In this case, the effective annual rate for the $15,000 loan, with a 12% nominal interest rate and $1,800 deducted upfront, is 13.64%.

Step-by-step explanation:

The question asked pertains to the concept of discount interest and requires calculating the effective annual rate when the interest is deducted from the principle at the beginning of the loan period. To find the effective annual rate, we would take the total interest paid and divide it by the actual amount received, and then adjust it to an annual rate. Since the borrower receives $13,200 but pays $1,800 in interest over the period of one year, the effective annual rate (EAR) can be calculated as follows:

EAR = (Interest / Actual money received) × 100

EAR = ($1,800 / $13,200) × 100

EAR = 0.13636... × 100

EAR = 13.64% (rounded to two decimal places)

The effective annual rate for the loan is therefore 13.64%.