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 are
annual, intra-year, and annuity compounding. This article discusses intra-year calculations for compound interest.
For additional information about annual compounding, view the following article:
Calculating Future Value of Intra-Year Compound Interest
Intra-year compound interest is interest that is compounded more frequently 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 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
Examples
The examples in this section use the EFFECT function, the general equation, and the following sample data:
|
Intra-Year compounding rate |
Number of compounding 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?
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.
Using the General Equation
The following example uses the general equation:
=100*(1+.08/2)^(2*3)
The example returns $126.53.
Calculate Interest Rates for Intra-Year 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
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.
Use the General Equation
The following equation returns the interest rate:
=(1+(.075/4))^(4*2)-1
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.
