Question

Calculate the effective interest rate for the following nominal interest rates:

a. Interest rate of 11% per year, compounded annually

b. Interest rate of 11% per year, compounded semi-annually

c. Interest rate of 11% per year, compounded quarterly

d. Interest rate of 11% per year, compounded daily e. Interest rate of 11% per year, compounded continuously

Answer 1

A. Interest rate of 11% per year, compounded annually

= ERI

= [ 1 + (Nominal Interest rate / period of compounding) ]  ^ period of compounding - 1

= [ 1 + (0.11/12)] ^ 12 - 1

= [ 1.00916 ]^12 - 1

= 1.115763 - 1

= 0.115763

= 11.5763 %

B. Interest rate of 11% per year, compounded semi - annually

= ERI

= [ 1 + (Nominal Interest rate / period of compounding) ]  ^ period of compounding - 1

= [ 1 + (0.11/6)] ^ 6 - 1

= [ 1.01833 ]^6 - 1

= 1.114948 - 1

= 0.114948

= 11.4948%

C. Interest rate of 11% per year, compounded quarterly

= ERI

= [ 1 + (Nominal Interest rate / period of compounding) ]  ^ period of compounding - 1

= [ 1 + (0.11/3)] ^3 - 1

= [ 1.0367 ]^3 - 1

= 1.11419 - 1

= 0.11419

= 11.419%

D. Interest rate of 11% per year, compounded daily

= ERI

= [ 1 + (Nominal Interest rate / period of compounding) ]  ^ period of compounding - 1

= [ 1 + (0.11/365)] ^365 - 1

= [ 1.000301 ]^365 - 1

= 1.11626 - 1

= 0.11626

= 11.626%

E. Interest rate of 11% per year, compounded continuously

= ERI

= e^r - 1

= (2.72)^0.11 - 1

= 1.116356 - 1

= 11.6356 %