The concept of compound interest or compounding interest is the interest is added back to the principal sum while charging interest for the next period so that interest is earned on that added interest. That is as a result of reinvesting interest, compound Interest (CI) / Cumulative Interest are calculated both on the principal amount and prior interest earned.

Compound interest is generally charged more than once during a year viz. monthly, quarterly(once in three months), half yearly (once in six months) or annually (once in a year) and earned interest for the above period is reinvested.

Annual compounding interest formula is, A= P(1+R/N)^{NT}

Where A= Future value of the investment/loan including interest.

Where P=Principal amount, R=rate of interest decimal), N=number of time interest is compounded in a year. T=time (number of years money invested or borrowed for)

Or Total compound interest= P (1+R/N)^{NT}-P

Illustration: 1

Let us take an example of loan/deposit amount of Rs.10000.00, Interest rate is 5% (i.e.5/100= 0.05) per year, interest is compounded monthly, period of loan/deposit is 10 years then compound interest on the loan for 10 years is;

P = 10000. R = 5/100 = 0.05 (decimal). N =12, T = 10

If we club these figures into the formula, we get:

A = 10000 (1 + 0.05/ 12) ^{12×10}=16470.10

The compound interest= 16470.10-10000=6470.10

So, the investment balance after 10 years is Rs.16470.10 and compound interest earned is Rs.6470.10.

Illustration: 2

In case interest is compounded once in a year we need to compound the interest with the following formula

A=P (1+R) ^{T}

Let us take another example off P=10000, interest is 5% per year compounded once a year deposit is for 3 years.

A=P(1+R)^{T}

A=10000(1+0.05)^{3 =10000(1.05)3}

=10000[1.157625] =11576

So, the investment balance after 3 years is Rs.11576 and compound interest earned for 3 years is Rs.1576.