Banks sometimes quote interest rates in the form of “add-on interest.” In this c

Question

Banks sometimes quote interest rates in the form of “add-on interest.” In this case, if a 1-year loan is quoted with a 13.0% interest rate and you borrow $1,000, then you pay back $1,128. But you make these payments in monthly installments of $94 each.

What is the true APR on this loan? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Use a financial calculator or Excel.)

What is the effective annual rate on the loan? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Banks sometimes quote interest rates in the form of “add-on interest.” In this case, if a 1-year loan is quoted with a 13.0% interest rate and you borrow $1,000, then you pay back $1,128. But you make these payments in monthly installments of $94 each.

Explanation / Answer

EMI:

= [P×r×(1+r)^n]÷[(1+r)^n-1]

$94 = [$1,000×r×(1+r)^12]÷[(1+r)^12-1]

r = 0.01902

APR = 0.01902×12 = 0.22824 or 22.82%

EAR = (1+0.01902)^12-1 = 25.37%

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