What is the difference between effective, real and nominal interest rate?

Question

I have been somewhat confused in financial math when to change the rates and the difference between effective, real and nominal rates. I still am confused after searching on Google and asking the teacher, so I was wondering if anyone had a more simplistic way of explaining it to get the overall idea. Thank you!

Answer 1

The nominal interest rate is the interest rate that does not take into account the effects of compound interest (or inflation, for that matter). I like to think about it in this way: say I put $\$1000$ in the bank that offers me a $5\%$ compound interest rate each month (my bank is very generous). Then, if I didn't know what compound interest was, I might assume that the interest accrued would be $12 \times 5 = 60\%$. The nominal annual interest rate in this case would be $60\%$.

However, this figure of $60\%$ does not take into account the effects of compound interest. In actual fact, after $1$ year my $\$1000$ would turn into $$ 1000 \times 1.05^{12} = \$1796 > \$1600 $$ So rather than going up by $60\%$, by money actually went up by $79.6\%$ (to one decimal place). This figure of $79.6\%$ is the effective interest rate-the interest accrued over the course of a year once the effects of compound interest have been taken into account.

Finally, the real interest rate is the interest rate once the effects of inflation have been taken into account. $\$1796$ might be the amount of money that you have after a year, but in that years the prices of goods will have risen, meaning that in practice $\$1796$ is worth less than it used to be.