Compound Interest For Different Compounding Periods

I. Introduction

We saw how to calculate compound interest where interest is compounded every year. But it is possible that interest is compounded at different periods like monthly or quarterly.

Let us see how to do that.

We can take the example of compounding every quarter (that is three months).

Let us say your bank account, gives an annual interest of $R%$, compounded every quarter.

So the interest is $\dfrac{R}{4}%$ every compounding period.

At the end of the first compounding period the amount $(A)$

$A = P\left(1+\dfrac{R}{4 \times 100}\right)$

Similarly at the end of the second quarter,

$A = P\left(1 + \dfrac{R}{4 \times 100}\right)^2$

At the end of one year the total amount will be,

$A = P\left(1 + \dfrac{R}{4 \times 100}\right)^4$

Therefore, at the end of $N$ years, the amount will be:

$A = P\left(1 + \dfrac{R}{4 \times 100}\right)^{4N}$

-----------book page break-----------

Therefore, generalizing this, if a compound interest is paid $n$ times a year, or in other words $n\ is\ the\ compounding\ frequency$, then the interest paid every compounding period will be $\dfrac{R}{n}\%$ and the amount after $N$ years will be:

$A = P\left(1 + \dfrac{R}{n \times 100}\right)^{nN}$

where,

$P = the\ principal\ amount$,

$R = the\ annual\ rate\ of\ interest\ in\ \%$,

$n = the\ compounding\ frequency$,

$N = the\ total\ time\ in\ years$, and

$A = the\ total\ amount\ after\ N\ years$

Compound interest is a calculation intensive exercise. Since it involves exponents of fractions, it is very difficult to do this manually for more than 2 or 3 compounding periods. These calculations are done using the log table, which you will learn at a higher grade.

For now, the problems that you encounter in our practice/assessment sessions will contain sufficient calculation aids to enable you to solve the whole problem in a reasonable time, without using any external aid.