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
=
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%
