Aptitude

Compound interest in short is **interest on interest**.

This is the sum of money invested or the amount we borrow from the bank or someone.

This represents the rate of interest (generally in per annum). It is used to calculate the interest amount.

This is the time for which the principal is invested or borrowed.

This is the amount that is calculated on the principal using the rate of interest and the time of investment.

Lets take an example to understand compound interest better.

Lets say we have invested Rs. 1000 at 10% p.a. for 2 years as compound interest.

So, principal P = 1000, rate R = 10 and time n = 2.

Now, lets find the compound interest.

```
1st year
--------------------
Principal for 1st year P = 1000
Rate R = 10
Interest I = PRn/100, where n = 1 as we are calculating interest for 1 year
or, I = (1000 x 10 x 1) / 100
= 100
Amount at the end of 1st year
A = P + I
= 1000 + 100
= 1100
2nd year
--------------------
Principal for 2nd year = Amount at the end of 1st year
P = 1100
Rate = 10
Interest I = PRn/100, where n = 1 as we are calculating interest for 1 year
or, I = (1100 x 10 x 1) / 100
= 110
Amount at the end of 2nd year
A = P + I
= 1100 + 110
= 1210
```

So, after 2 years of investment the principal Rs. 1000 amounts to Rs. 1210.

So, compound interest earned in 2 years on Rs. 1000 at 10% p.a. is (1210 - 1000) i.e. Rs. 210.

Simple Interest for 1 years and Compound interest for 1 year for a given principal and rate of interest are both equal.

This means we are calculating the interest once a year.

This means we are calculating the interest twice a year.

This means we are calculating the interest 4 times a year.

This means we are calculating the interest every month for a year.

```
We have,
Principal P = 1000
Rate R = 10
Time n = 2
Since, the interest is compounded annually
so, we are calculating interest once a year.
Amount A = P ( 1 + R/100 )
```^{n}
= 1000 ( 1 + 10/100 )^{2}
= 1000 ( 1.1 )^{2}
= 1000 x 1.21
= 1210
So, compound interest CI = A - P
= 1210 - 1000
= 210

So, the compound interest after 2 years of investment is Rs. 210.

```
We have,
Principal P = 1000
Rate R = 10
Time n = 2
Since, the interest is compounded half-yearly
so, we are calculating interest twice a year.
Amount A = P ( 1 + ((R/2) / 100) )
```^{2n}
= 1000 ( 1 + ((10/2) / 100) )^{2x2}
= 1000 ( 1 + (5/100) )^{4}
= 1000 ( 1.05 )^{4}
= 1000 x 1.21550625
= 1215.51
So, compound interest CI = A - P
= 1215.51 - 1000
= 215.51

So, the compound interest after 2 years of investment is Rs. 215.51.

Try this yourself.

Answer: Rs. 218.40

Try this yourself.

Answer: Rs. 220.39

Feel free to check out Compound Interest calculator.