XL: How to Calculate Compound Interest for an IntraYear Period

ID: Q162634

The information in this article applies to:

Microsoft Excel 97 for Windows
Microsoft Excel for Windows 95, version 7.0
Microsoft Excel for Windows, versions 5.0, 5.0c

SUMMARY

The future value of a dollar amount, commonly called the compounded value, involves the application of 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 discusses intrayear calculations for compound interest.

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

Q141695 XL: How to Calculate Compound Interest

MORE INFORMATION

Calculating Future Value of Intrayear Compounded Interest

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

Microsoft Excel 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 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)

where the following is true:

P = initial principal
k = annual interest rate paid
m = number of times per period (typically months) 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 following sample data.


 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

REFERENCES

For more information about compound interest, click the Index tab in Microsoft Excel 97 Help, type the following text

compound interest

and then double-click the selected text to go to the "Effect" topic.

For more information about the EFFECT worksheet function in Microsoft Excel version 7.0, click Answer Wizard on the Help menu and type:

effect

For more information about the EFFECT worksheet function in Microsoft Excel version 5.0, choose the Search button in Help and type:

effect

Additional query words: 97 XL97

Keywords : xlformula xladdin
Version : WINDOWS:5.0,5.0c,7.0,97
Platform : WINDOWS
Issue type : kbhowto