# Introduction to Compound Interest

When learning about Compound Interest it is important to remember that money is not returned on an annual basis only. Very often people repay money on a half yearly or quarterly basis too. In each scenario, the interest compounded will be calculated differently.

There are three various ways in which interest can be compounded.

Compounded annually: under this, interest is calculated for an entire year.

Compounded half yearly: under this, interest is calculated for six months. This means that money is taken out after six months and reinvested later for another six months. So the rate in this period becomes half of the actual rate and the time periods are doubled.

Compounded quarterly: under this, the interest is calculated for every quarter of the year. This means that money is taken out after three months reinvested for another three months. Thus the rate in this period is becomes 1/4 of the actual rate and the time periods is quadrupled.

Next, we will talk about different time periods. Say we assume a rate of interest as 20% and time as 2 years. For compounding annually, the rate will be 20% p.a. while the time periods shall be 2 (for 2 years).

For the second case, i.e. compounding half-yearly, the rate of interest will be 10% p.a. which will be calculated 4 times ( time period in 2 years is 4).

While for the last kind, the rate of interest will be 5% p.a. and time period 8.

Moving on, let us solve some examples based on the above explained concepts.

Compounding Annually:

Q) Given that the principal is Rs. 10,000, rate 20% and time period 2 years, find the interest on the principal after the stipulated time.

Using the formula

Amount = P (1 + R/100) ^ T

We have 10,000 x (1 + 20/100)^2 which amounts to Rs. 14,400. Subtracting the principal from the amount we get the interest which is Rs. 1,440.

Compounding Half- Yearly:

Q) Same as above. Only the time period is 1 year instead of 2 years.

The rate will be reduced by half making it 10% whereas the time period will be doubled.

So Amount = 10,000 x (1 + 10/100)^2 that is Rs. 12,100. To get the interest we will subtract the principal from the amount resulting in Rs. 2,100.

Compounding Quarterly:

Q) Same as above with the time period as 9 months. The rate will be taken as 5% while the time periods will change to 3.

Solving further,

10,000 (1 + 5/100)^3

=>10,000 (21/20) (21/20) (21/20)

=> 3176.25

Hence the amount is Rs. 3,176.25

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