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How to calculate compound interest for an intra-year period in Excel

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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 areannual, intra-year, and annuity compounding. This article discusses intra-year calculations for compound interest.

For additional information about annual compounding, click the article number below to view the article in the Microsoft Knowledge Base:
141695 XL: How to Calculate Compound Interest
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Calculating Future Value of Intra-Year Compound Interest

Intra-year compound interest is interest that is compounded more frequently thanonce a year. Financial institutions may calculate interest on bases ofsemiannual, quarterly, monthly, weekly, or even daily time periods.

Microsoft Excel includes the EFFECT function in the Analysis ToolPak add-in for versions older than 2003. The Analysis ToolPak is already loaded. 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 intra-year compound interest with the EFFECT worksheet function is as follows:
=P+(P*EFFECT(EFFECT(k,m)*n,n))
The general equation to calculate compound interest is as follows
=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
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Examples

The examples in this section use the EFFECT function, the generalequation, and the following sample data:
   Intra-Year                 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 percent compounded semiannually. If the money is left in the account for three years, how much will the $100 be worth?

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Use 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 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.

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Using the General Equation

The following example uses the general equation:
=100*(1+.08/2)^(2*3)
The example returns $126.53.

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Calculate Interest Rates for Intra-Year Compounding

You can find the compounded interest rate given an annual interest rateand 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, usethe following equation:
=(1+(k/m))^(m*n)-1
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Examples

Use the EFFECT Worksheet Function

An investment of $100 pays 7.50 percent compounded quarterly. The money is left in the account for two years, for example. The following formula returns the compounded interest rate:
=EFFECT(EFFECT(.075,4)*2,2)
The example returns 16.022 percent.

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Use the General Equation

The following equation returns the interest rate:
=(1+(.075/4))^(4*2)-1
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References
For more information about compound interest, click Microsoft Excel Help on the Help menu, type effect in the Office Assistant or the Answer Wizard, and then click Search to view the topic.
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XL2000 XL2002 XL2003 XL2007 XL2007 XL2010 Future Value Intra Year Compound Interest formula kbhowto
Properties

Article ID: 213907 - Last Review: 09/23/2015 06:29:00 - Revision: 7.0

Microsoft Excel 2000 Standard Edition, Microsoft Excel 2002 Standard Edition, Microsoft Office Excel 2003, Microsoft Excel 2010, Microsoft Office Excel 2007, Excel 2016, Microsoft Excel 2013

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