Investment Science: Effective and Nominal interest rates

Sunday, August 15, 2010

In this post, we will see the difference between the effective and nominal interest rates, if you are a beginner, I would strongly recommend you to refer to the concept of compound interest in this article, note that the understanding of interest rates and how it's compounded is very crucial in investments as investment science makes sense only if there is an interest rate involved, isn't it?

As mentioned earlier, interest rate can be compounded yearly, monthly or quarterly, therefore if you have an investment which is compounded 'm' periods per year, then it's easy to ask a question "What is the yearly interest rate for an investment compounded 'm' periods per year", accordingly, we define two interest rates

1. Nominal interest rate 'r' compounded 'm' periods per year - Here the investment grows by (1 + r/m) per period and (1 + r/m) ^ m per year.
2. Effective interest rate (r') which is the equivalent yearly rate for the nominal interest rate 'r' - Here the investment grows by (1 + r') per year.

Therefore the relationship between effective interest rate and nominal interest rate should be derived from

For example, given an interest rate of 10% compounded quarterly, what is the effective interest rate?

Here r = 10%, m = 4, therefore the effective interest rate

r' = (1 + 0.1 / 4) ^ 4 - 1 = 10.381%

Also, when it comes to continuous compounding (where the compounding period m -> Infinity), then the relationship between effective interest rate (r') and nominal interest rate (r) is given by

Note, when compounded continuously with an interest rate of 10%, the effective interest rate will be

r' = e ^ (10/100) - 1 = 10.517%

Therefore continuous compounding will always be beneficial.

In the next post, we will see look into the present value and the future value of an investment.

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