Question

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

Answer 1

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

Answer a

.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%

Answer b

.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%

​​​​​​​Answer c

.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%

​​​​​​​Answer d

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%