Why do Effective Interest Rates yield more than Nominal Interest Rates?

The interest rates paid annually by financial organizations on an annual basis are known as Nominal Interest Rates. In such an arrangement, the interest is paid at the end of each year. If compounding is done, that will also be covered under this arrangement in one shot.

However, there are arrangements in which financial organizations pay interests on funds semi-annually or quarterly. For example, in the case of loans, the charges or interests may be levied semi-annually. Such an arrangement of paying the interest several times within a selected period is known as Effective Interest Rates.

Nominal Interest Rate Vs Effective Interest Rate

As is obvious, effective interest rates yield more interest rates than the nominal rate. As the number of periods is increased in nominal compounding, the net interest rate goes up in such arrangements. Usually, the calculations are done at the start of each period of the financial arrangement.

For example, in case of a semi-annual arrangement, the interest rates are applied first on the first six months and then the calculations are done for the next period. So, the number of periods on which the accounting is done increases from 1 to 2 in such a case. Similarly, in case of a quarterly arrangement, the number of periods would be 3.

Note − The investments would grow in case of both nominal and effective interest rates, but since the number of payments (periods) go up, the effective rate also goes up in case of effective interest rates.

How Does the Interest Rate Increase in Effective Interest Rate?

The following calculation shows how the interest goes up in case of the effective interest rate.

Suppose an investment of INR 100 is made at a bank at a rate of interest of 20% on a semi-annual basis. How much will the investment yield at the end of the year?

Let us first consider the first semi-annual return.

The interest for first six months = 100 × 20% × 1/2 = INR 10

Now at the beginning of the next cycle, the principal would be INR 110 and the interest would be paid on 110, not 100.

So, the interest becomes, 110 × 20% × 1/2 = 11

The total money accumulated will be = 100+10+11= INR 121

There is an increase in returns while Effective Interest Rate is considered.

One would have received an amount of INR 120 from the nominal rate of interest. But, the effective rate has increased the rate of return at a rate of 11/100 = 11%.

This means that an investment compounded semi-annually of INR 100 at the rate of 10% is equal to an investment at the rate of 10.25% done annually.

Note − Nominal interest rate is always less than Effective interest rates due to the fact that the number of periods considered is more in the case of effective rate.