Question

Problem 5-60 Effective Interest Rate (L04) Find the APR (the stated interest rate) for each case. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.) APR Effective Annual Compounding Interest Rate Period 16.77 % 1 month 7.12 6 months 10.38 3 months % % %

Answer 1

1). APR = m * [(1 + ear)^1/m - 1]; m = no. of compounding periods in a year

a). APR = 12 * [(1 + 0.1677)^1/12 - 1]

= 12 * [1.013 - 1] = 12 * 0.013 = 0.1560, or 15.60%

b). APR = 2 * [(1 + 0.0712)^1/2 - 1]

= 2 * [1.0350 - 1] = 2 * 0.0350 = 0.07, or 7.00%

c). APR = 4 * [(1 + 0.1038)^1/4 - 1]

= 4 * [1.025 - 1] = 4 * 0.025 = 0.10, or 10.00%

2). APR = Periodic rate * No. of compounding periods in a year = 1.03% * 52 = 53.56%

EAR = [1 + Periodic rate]^{No. of compounding periods in a year} - 1

= [1 + 0.0103]⁵² - 1 = 1.7038 - 1 = 0.7038, or 70.38%