Question

Effective Annual Rate (EAR) problems. Remember, percentages must be to 2 decimal places.ch 5.25%: a. Abe has a credit card that has an annual percentage rate (APR) of 21% Interest is compounded monthly Calculate the EAR. b. From question "*". Calculate the EAR if interest is compounded weekly (assume 52 weeks.) c. From question "a". Calculate the EAR if interest is compounded continuously. d Barb has a loan which has an APR of 6%. Interest is compounded semi-annually. Calculate the EAR

Answer 1

Effective Annual Interest Rate(EAR) = [{1+(i/k)}^k]-1

where, i = APR, k = Number of times compounded

6.

a.

EAR = [{1+(0.21/12)}^12]-1 = 0.2314 = 23.14%

b.

EAR = [{1+(0.21/52)}^52]-1 = 0.2332 = 23.32%

c.

EAR(if continuously compounded) = e^i -1(where, e=2.71828(constant))= e^0.21-1 = 1.2337-1 = 0.2337 = 23.37%

d.

EAR = [{1+(0.06/2)}^2]-1 = 0.0609 = 6.09%

e.

APR = Monthly Rate*12 = 20*12 = 240%

EAR = [{1+(0.2)}^12]-1 = 7.9161 = 791.61%