Microsoft KB Archive/186004

= XL98: How to Calculate Compound Interest for an IntraYear =

Article ID: 186004

Article Last Modified on 9/11/2002

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APPLIES TO


 * Microsoft Excel 98 for Macintosh

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This article was previously published under Q186004



SUMMARY
Calculating the future value of a dollar amount, commonly called the compounded value, requires applying compound interest to a present value amount. The result is a future dollar amount. Three types of compounding include: annual, intrayear, and annuity compounding. This article contains information about intrayear calculations for compound interest.

For additional information about annual compounding, please see the following article in the Microsoft Knowledge Base:

141695 XL: How to Calculate Compound Interest



MORE INFORMATION
Intrayear compound interest is interest that is compounded more often than once per year. Financial institutions may calculate interest on the basis of semiannual, quarterly, monthly, weekly, or even daily time periods.

Microsoft Excel 98 Macintosh Edition includes the EFFECT function in the Analysis ToolPak add-in. The EFFECT function returns the compounded interest rate based on the annual interest rate and the number of compounding periods per year.

The formula to calculate intrayear compound interest by using the EFFECT worksheet function is the following:

=P+(P*EFFECT(EFFECT(k,m)*n,n))

The general equation to calculate compound interest is the following:

=P*(1+(k/m))^(m*n)

For this equation, the following is true:

P = initial principal

k = annual interest rate paid

m = number of times per period (typically years) the interest is compounded

n = number of periods (typically years) or term of the loan

Examples
The examples in this section use the EFFECT function, the general equation, and the sample data that is listed in the following table.   IntraYear                 Number of compounding compounding rate         periods per year ---  Semiannual                  2 Quarterly                  4 Monthly                   12 Weekly                    52 Daily                    360 or 365(actual) An investment of $100 pays 8.00% compounded semiannually. If the money is left in the account for 3 years, how much will the $100 be worth?

Example Using the EFFECT Worksheet Function:

Because of semiannual compounding, you must repeat the EFFECT function twice to calculate the semiannual compounding periods. In the following example, the result of the nested function is multiplied by 3 in order to spread out (annualize) the compounded rate of over the term of the investment:

=100+(100*EFFECT(EFFECT(.08,2)*3,3))

The example returns $126.53.

Example Using the General Equation:

The following example uses the general equation:

=100*(1+.08/2)^(2*3)

The example returns $126.53.

Calculating Interest Rates for Intrayear Compounding
You can find the compounded interest rate given an annual interest rate and a dollar amount.

The EFFECT worksheet function uses the following formula:

=EFFECT(EFFECT(k,m)*n,n)

To use the general equation to return the compounded interest rate, use the following equation:

=(1+(k/m))^(m*n)-1

Examples
Example Using the EFFECT Worksheet Function:

An investment of $100 pays 7.50% compounded quarterly. The money is left in the account for 2 years For example, the following formula returns the compounded interest rate:

=EFFECT(EFFECT(.075,4)*2,2)

The example returns 16.022%.

Example Using the General Equation:

For example, the following equation returns the interest rate:

=(1+(.075/4))^(4*2)-1

The example returns 16.022%.

