Question

# Find the APR, or stated rate, in each of the following cases (Do not round intermediate...

 Find the APR, or stated rate, in each of the following cases (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.):
 Stated Rate (APR) Number of Times Compounded Effective Rate (EAR) % Semiannually 12.1 % Monthly 13.0 Weekly 10.7 Infinite 14.4

Effective Annual RAte (EAR) = (1+(APR/no. of compounding per year))^no. of compounding per year -1

.121 = (1+(APR/2))^2 -1

(1+(APR/2))^2 = 1.121

1+(APR/2) = 1.121^(1/2)

= 1.05877287461

APR/2 = 1.05877287461-1 = .05877287461

APR = .05877287461*2

= 11.75%

.13 = (1+(APR/12))^12 -1

(1+(APR/12))^12 = 1.13

1+(APR/12) = 1.13^(1/12)

= 1.01023684436

APR/12 = 1.01023684436-1 = .01023684436

APR = .01023684436*12

= 12.28%

.107 = (1+(APR/52))^52 -1

(1+(APR/52))^52 = 1.107

1+(APR/52) = 1.107^(1/52)

= 1.00195678998

APR/52 = 1.00195678998-1 = .00195678998

APR = .00195678998*52

= 10.18%

EAR = e^APR -1

.144 = e^APR -1

e^APR = 1.144

2.71828^APR = 1.144

APR = log 1.144 / log 2.71828

= 0.05842602445/0.43429418977

= 13.45%

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