Money market and the equilibrium nominal interest rate

Key Questions

• What is the effective interest rate?

  Answer:

  The rate of interest at which a sum actually grows if compounding occurs more than once a year.

  Explanation:

  You deposit a sum of money in a bank that pays 8% interest a year, compounded yearly. (Those were the good-old days for depositors).

  I deposit my money in another bank that pays 8% a year, but it is compounded every 3 months - quarterly. So, at the end of every 3 months the bank gives me interest. At the end of the year, who will have the most money in their account?

  I will because at the end of the first 3 months I receive interest and then at the end of the next 3 months I will receive interest on my original deposit plus interest on the interest I have already earned...and so on for the year.

  We can use a simple formula to calculate the actual or effective interest rate that I received.

  #(1 + (m/n)^n) - 1#

  Where
  M = the yearly or nominal rate - 8% in this case.
  N = the number of times a year compounding occurs.

  My effective rate is

  #(1 + (.08)/4)^4 - 1)#

  8.24% and yours was 8% (we could prove this using the formula).

  John · 2 · Jul 4 2015

• What is the effective interest rate?