## Effective and Nominal Rate of Interest

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In compound interest case, interest earned in the previous year also earns interest.

If the interest is paid once per unit time at the end of the period, it is called effective rate of interest. Or it is the actual interest rate paid per measuring period.

A nominal rate of interest is the interest rate for a period, but interest is paid more or less than once per measurement period. If interest is calculated p times per measuring period, then a nominal interest rate i means that an effective interest rate of i/p is paid p times in a measuring period.

The relation between nominal and effective interest rate is given below.

Where
i_{eff} is the effective interest rate per period, i is the nominal
interest rate per period, p is the number of times interest is calculated per
period.

#### Numerical Problem

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Q. 1. Calculate the effective rate of interest if the interest rate pa is 10% and payable quarterly.

Q. 2. If Rs. 1000 is invested in an account that pays nominal interest rate of 10% pa convertible half yearly. Calculate the accumulated amount in the account after 2 years.