Question

Find the APR, or stated rate, in each of the following cases (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)): Stated Rate (APR) Number of Times Compounded Effective Rate (EAR) % Semiannually 12.2 % Monthly 13.1 Weekly 10.8 Infinite 14.5.

Answer 1

Answer:

Stated Rate    No. of Times Compounded     Effective Rate (EAR) %            

   11.85%                    Semiannually                             12.2 %

   12.37%                    Monthly                                      13.1%

   110.27%                    Weekly                                       10.8%

   13.54%                    Infinite                                        14.5%

Explanation:

EAR = ( 1 + ( APR / m )^m)-1

Semiannually

m = 12 / 6 = 2

0.1220 = ( ( 1 + ( APR / 2 ) )^2) - 1

0.1220 + 1 = (1 + ( APR / 2 ) )^2

1.1220 = ( 1 + ( APR / 2 ) )^2

$\sqrt{1.1220}$ = $\sqrt{( 1 + ( APR / 2 ))^2}$

1.059 = 1 + ( APR / 2 )

1.059 - 1 = APR / 2

0.059 x 2 = APR

APR = 0.1185 = 11.85%

Monthly

m = 12  / 1 = 12

0.1310 = ( ( 1 + ( APR / 12 ) )^12) - 1

0.1310 + 1 = (1 + ( APR / 12 ) )^12

1.1310 = ( 1 + ( APR / 12 ) )^12

APR = 12.37%

Weekly

m = 52

0.1080 = ( ( 1 + ( APR / 52 ) )^52) - 1

0.1080 + 1 = (1 + ( APR / 52 ) )^52

1.1080 = ( 1 + ( APR / 52 ) )^52

APR = 10.27%

Infinite

m = 20,000

0.1450 = ( ( 1 + ( APR / 12 ) )^12) - 1

0.1450 + 1 = (1 + ( APR / 12 ) )^12

1.1450 = ( 1 + ( APR / 20,000 ) )^20,000

APR = 13.54%