Question

Find the APR, or stated rate, in each of the following cases: a. An effective interest of 6% compounded semiannually b. An effective interest of 6% compounded monthly

Answer 1

a). Effective annual rate = 6%

So, APR = n*((1+EAR)^(1/n) - 1)

needed, APR compounded semiannually, so here, n = 2

So, APR = 2*((1.06^(1/2)) - 1) = 5.91%

b). Effective annual rate = 6%

So, APR = n*((1+EAR)^(1/n) - 1)

needed, APR compounded monthly, so here, n = 12

So, APR = 12*((1.06^(1/12)) - 1) = 5.84%

c). Effective annual rate = 10%

So, APR = n*((1+EAR)^(1/n) - 1)

needed, APR compounded weekly, so here, n = 52

So, APR = 52*((1.10^(1/52)) - 1) = 9.54%

d). Effective annual rate = 13%

For APR compounded continously,

APR = ln(1+EAR)

So, APR = ln(1.13) = 12.22%