CAT 2025 Lesson : Interest & Growth - Basics of Compound Interest

3. Compound Interest

In Compound Interest, interest rate is applied on the principal as well as the interest accrued over the prior periods.

A key aspect, therefore, is the rate or speed of compounding. Typically the compounding period for interest is specified. In questions where it is not specified, the assumption is that the interest is compounded annually.

The Compound Interest formula is to calculate the amount, which is the sum of principal and interest. Note that the Simple Interest formula was to compute the interest only.

$A = p \left(1 + \dfrac{r}{100}\right)^{n}$

where, $A =$ Amount (Principal + Interest)
$p =$ Principal
$r =$ Rate of interest in percentage for a time period
$n =$ Number of time periods for which the interest is to be compounded


The following table provides the simple and compound interest at $10 \%$ per annum for a principal of Rs. $1,000$.

Year	Simple Interest			Compound Interest
	Principal	Interest	Amount	Principal	Interest	Amount
1	1,000	100	1,100	1,000	100	1,100
2	1,000	100	1,200	1,100	110	1,210
3	1,000	100	1,300	1,210	121	1,331
4	1,000	100	1,400	1,331	133.1	1,464.1

In Simple Interest, interest of $10 \%$ was computed on the initial principal amount of Rs. $1,000$. The interest of Rs. $100$ per year did not change across the years.

In Compound Interest, the following are to be noted.
$\blacktriangleright$ In the first year, Simple Interest = Compound Interest.
$\blacktriangleright$ The principal includes the interest earned till the previous year (or period).
$\blacktriangleright$ The amount due (principal + interest) at the end for a certain period is the principal for the next period.
$\blacktriangleright$ The Compound Interest for successive periods increases at the interest rate.
(For instance, the interest amounts are Rs. 100, Rs. 110, Rs. 121, ..., which is increasing at 10 $\%$ p.a.)