If $5,000 is borrowed on a discount basis and the rate is 10 percent, the annual percentage interest rate on this loan would be

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Quizplus · Accepted Answer

On a discount basis, the interest is deducted upfront from the principal amount. Therefore, the amount borrowed is the present value, and the interest is the discount. Let D be the discount, then D = P*r*t where P is the principal, r is the rate, and t is the time in years. In this case, D = 5,000*0.1*1 = 500. So, the amount received is 5,000 - 500 = 4,500. The APR is the effective annual rate of interest, taking into account the compounding effect of interest. Since there is no compounding in this case, the APR is simply the ratio of interest to the amount borrowed, expressed as a percentage. APR = D/P*100 = 500/5,000*100 = 10%. However, the APR is not the same as the nominal or stated rate of interest, which is the rate quoted by the lender. The nominal rate is only relevant for comparing different loan offers, and it does not reflect the true cost of borrowing. The true cost is reflected in the APR, which includes all the fees and charges associated with the loan. Therefore, the best choice is D, 11.1%, which is the true cost of borrowing on a discount basis.

If $5,000 Is Borrowed on a Discount Basis and the Rate