Question

a.  If you are told that your effective annual interest rate is 10%, what is the nominal interest rate compounded quarterly?

b.  What is the effective annual interest rate if the nominal interest rate is 7%, and the frequency of compounding is once a month?

c.  How much time would it take for your principal to quadruple if the effective annual interest rate is 5%, and the frequency of compounding is once a year?

Answer 1

A) Effective annual interest rate = [1 + (i/n)]ⁿ - 1

Where, i = nominal interest rate; n = no. Of times interest rate is compounded each year

Therefore, 10% = [1 + (i/4)]⁴ - 1

Or, 0.1 = [1 + (i/4)]⁴ - 1

Or, [1 + (i/4)]⁴ = 1.1

Or, 1 + (i/4) = (1.1)^(1/4) = 1.024

Or, (i/4) = 0.024

Or, i = 0.096 = 9.6%

Answer: 9.6%

B) i = 7% and n = 12

Effective annual interest rate = [1 + (7%/12)]¹² - 1 = 7.23%