6a- Types of frequencies of compounding.

Last Updated on September 6, 2026 by Maged kamel

Types of frequencies of compounding.

The compounding frequency is the number of times per year (or, rarely, another unit of Time) that accumulated interest is paid out or capitalized (credited to the account).

The frequency could be yearly, half-yearly, quarterly, monthly, weekly, daily, or continuously (or not at all, until maturity). Quoted from the definition of compound interest.

The balance of $1 is compounded semiannually at 100% per annum.

This is the semiannual type of compounding. In the last semiannual period, the future value of $1 compounded annually.

After one year,,,, based on compound intere at at, 100% compounded yearly. The value was $2.00; we want to find the balance based on 100% compounded semiannually. The first semiannual focal value at Time t1 = semiannual (1 semiannual period). We can see from the graph that Fv-1 = (1 + 2) * 0.50 = 1.50.

For the value of FV-2 after one year. We get the multiplication factor for the semiannual period was (1.50)^2/1.00 = $2.25.

Compounding begins after a semiannual period, and the slope increases according to the new ratio. Th s is the process of changing from a linear to an exponential function at t = 0.50 years.

Recall that the Fv equation=P0*(1+i)^n. In this case p0=$1, new i/n=(100/100)/2=50%. The power raised is (i*t) = 2*1 = 2.00. The future value obtained matches the value in Table 4.13. th FV-2=(1.5*1.5)/1=$2.25.

The balance of $1 for interest at 100%, compounded quarterly.

This is the second type of compounding: quarterly.

From the last post, we estimated the future value of $ after one year based on a compound interest rate of 100% compounded yearly. The value was $2.00; we want to find the balance after 100% compounded quarterly.

For the value of FV-2 after one year. We get the multiplication factor for the value at t=1 quarter of a year, which is=1.25.

The slope increases based on the new ratio. Th s is the process of changing from a linear to an exponential function at t = 0.25 years.

Recall that the FV equation is P0* (1+i)^n. In this case P₀=$1, new i/n=(100/100)/4=25%. The power raised is (i*t) = 4*1 = 4. The value obtained matches the value in Table 4.13. th FV-2=(1.25*1.25)/2=$2.4414.

The balance of $1 for interest at 100%, compounded monthly.

This is the third type of compounding monthly. In the last post, we estimated the future value of $1 after 1 year at a compound interest rate of 100% per year. The value was $2.00; we want to find the balance after 100% compounded monthly.

For the value of FV-2 after one year. We get the multiplication factor for the value at t=1 month of a year, which is=1.083333.

Compounding starts after the first month, and the slope increases based on the new ratio. Th s is the process of changing from a linear to an exponential function at t = = (1/12) year.

Recall that the FV equation is P0* (1+i)^n. In this case P₀=$1, new i/n=(100/100)/12=8.3333%. The power raised is (i*t) = 12*1 = 12. The value obtained matches the value in Table 4.13. th FV-2=(1.08333*1.08833)/1=$2.4414

The balance of $1 for the interest of100% compounded daily.

This is the fourth type of frequency, which is compounded daily. In the last post, we estimated the future value of $1 after 1 year at a compound interest rate of 100% per year. The value was $2.00; we want to find the balance after 100% compounded monthly.

For the value of FV-2 after one year. We get the multiplication factor for the value at t=1 day of a year, which is=1.0027397.

Compounding starts on the first day, and the slope increases based on the new ratio. Th s is the process of changing from a linear to an exponential function at t = (1/365) year.

Recall that the FV equation is P0* (1+i)^n. In this case P₀=$1, new i/n=(100/100)/365=2.739726*(10^-3). The power raised is (i*t) = 365*1 = 365.
The value obtained matches the value in Table 4.13. th FV-2=(1.0027397.*1.0027397)/1=$2.714567.

For a given rate of 6%, if the interest is compounded annually, it will be effective. At different frequencies, such as semiannually and quarterly, the interest value will change. The next slide shows these values.

When the number of years exceeds 1, it will be raised to a power and multiplied by I.

These are some examples of different interest rates, with different n values for years.

Solved example 3.7 to estimate the future value of a given deposit.

This is solved Example 3.7, for which it is required to estimate the future value for a given Po=$500, with 6% interest compounded quarterly, for n=3 years.

We can find the future value using Excel’s built-in function. See the following slide image.

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The previous post is Post 6: Introduction to compound interest.

The following post is Post 6 b: Introduction to a solved problem for compound interest

For a useful external resource, Engineering Economy is a good reference.