Question

7. A credit card company runs an ad quoting a nominal interest rate of 29 percent on charges. What is the effective interest rate if interest is compounded quarterly? monthly? The effective annual rate is ________if compounded quarterly and _______ if compounded monthly

Answer 1

Formula for effective interest rate is:

r = (1+i/n) ⁿ – 1        

r = Effective interest rate

i = Nominal interest rate = 29 % or 0.029

n = No. of compounding periods in a year

Requirement 1:

If n = 4

r = (1+ 0.029/4) ⁴ – 1

= (1+ 0.0725) ⁴ – 1

= (1.0725) ⁴ – 1

= 1.323089441 – 1

= 0.323089441 or 32.309 %

Requirement 2:

If n = 12

r = (1+ 0.029/12) ¹² – 1

= (1+ 0.024166667) ¹² – 1

= (1.024166667) ¹² – 1

= 1.33182647 – 1

= 0.33182647 or 33.183 %

The effective annual rate is 32.309 % if compounded quarterly and 33.183 % if compounded monthly.