In: Finance
Find the APR, or stated rate, in each of the following cases:
a. An effective interest of 18% compounded semiannually
b. |
An effective interest of 11% compounded monthly |
c. | An effective interest of 16% compounded weekly |
d. | An effective interest of 13% with continuous compounding |
The formula for APR is:
EAR = effective annual rate m = number of times the interest is compounding during the ear
a. An effective interest of 18% compounded semiannually
EAR = 18% = 0.18 m = 2
APR = 2 x [ (1 + 0.18)1/2 -1 ] = 2 x [ (1.18)1/2 -1 ] = 2 x [ 1.086278 -1 ] = 2 x 0.086278 = 0.1725561
APR = 17.26%
b. An effective interest of 11% compounded monthly
EAR = 11% = 0.11 m = 12
APR = 12 x [ (1 + 0.11)1/12 -1 ] = 12 x [ (1.11)1/12 - 1 ] = 12 x [ 1.00873459 - 1 ] = 12 x 0.00873459 = 0.10481513
APR = 10.48%
c. An effective interest of 16% compounded weekly
EAR = 16% = 0.16 m = 52
APR = 52 x [ (1 + 0.16)1/52 -1 ] = 52 x [ (1.16)1/52 - 1 ] = 52 x [ 1.00285831 - 1 ] = 52 x 0.00285831 = 0.148632
APR = 14.86%
d. An effective interest of 13% with continuous compounding
The formula for continuous compounding is
APR = ln(1+EAR)
EAR = 13% = 0.13
APR = ln(1+0.13) = ln(1.13) = 0.1222176 = 12.22%