Nominal Interest Rates

Interest rates may be quoted not cognisant of the effects of either inflation or compounding. Considering the effect of inflation, we arrive at what economists recognise as the real interest rate and, in the realm of compounding, we have effective interest rates.

Interest rates therefore that have not been adjusted for either inflation or compounding are referred to as nominal interest rates.

Knowing what a nominal interest rate is immediately obvious and the actual questions becomes what interest will we earn on our investment?

Effective interest rates

What is an effective rate of interest? It is the amount of interest that corresponds to the amount of interest we accrue or receive over a one calendar year period. For instance, if you receive interest of 5 currency units for every 100 unit investment over a one year period, it amounts to a 5% effective interest rate.

Let’s now suppose that your interest rate is 5% but compounded every six months. A 100 unit investment after six months will result in:

$100\times 5\% \times \frac{1}{2} = 2.5$

Investing this 2.5 along with the 100, results in $102.5\times 5\% \times \frac{1}{2} = 2.5625$ units

That means, for the same 100 investment, your investment have accumulated to $2.5625 + 102.5 = 105.0625$

Computing the additional interest earned as a result of compounding

With all inputs having remained the same, the difference of 0.0625 yield is as a result of compounding. Calculated as:

$105.0625 – 105.00 = 0.0625$

In order to quantify the effect of compounding, let’s next look at the two basic interest rate formulas in part 2.