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# Difference Between Nominal and Effective Interest Rate:

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1. What is difference between nominal and effective interest rate.
2. How effective interest rate is determined?

Contents:

## Explanation of the Difference:

Interest rates are typically stated as annual percentages. The stated annual rate is usually referred to as the nominal rate. Interest may be compounded semiannually, quarterly, and monthly, the interest earned during a year is greater than if compounded annually. When compounding is done more frequently than annually, an effective annual interest rate can be determined. This is the interest rate compounded annually which is equivalent to a nominal rate compounded more frequently than annually. The two rates would be considered equivalent if both result in the same compound amount.

## Formula of Effective Interest Rate:

Let r equal the effective annual interest rate, i the nominal annual interest rate, and m the number of compounding periods per year. The equivalence between the two rates suggests that if a principle P is invested for n years, the two compound amounts would be the same, or ## Example:

A small company has made a log-term investment of \$250,000. The interest rate is 12%, and interest is compounded quarterly.  Calculate annual effective interest rate.

### Solution:

 In this example the investment is made with a nominal interest rate of 12 percent per year compounded quarterly.  For this investment: i = 0.12 m = 4 The effective annual interest rate is calculated as follows: The effective annual rate is 12.551 percent *Future value of \$1 table - (1 + i)n table, we can determine that (1+0.03)4 = 0.12551 Practice Exercise:The nominal interest rate on an investment is 7 percent per year. What is the effective annual interest rate if interest is compounded semiannually? Answer: 7.122 percent

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## More study material from this topic: Methods for the evaluation of capital investment analysis Average rate of return or accounting rate of return method Cash payback method Net present value method Internal rate of return method Simple interest Future value of a single sum Future value of an annuity Present value of a single sum Present value of an annuity Qualitative consideration in capital investment analysis Capital investment analysis and unequal proposal lives Capital rationing decision process Difference between simple interest and compound interest Difference between nominal and effective interest rate Future value of \$1 table Present value of \$1 table Present value of ordinary annuity table Future value of ordinary annuity table

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