Compound Interest Explained with Simple Examples (and Why Starting Early Matters)

Compound interest is one of the most useful ideas in both maths exams and real life. In exams it appears in quantitative aptitude; in life it decides how much your savings grow. This guide explains it with simple rupee examples.

Simple interest first#

With simple interest, you earn interest only on the original amount (the principal).

where $P$ is the principal, $R$ the rate per year in percent and $T$ the time in years.

Example: ₹10,000 at 8% simple interest for 3 years: $SI = 10000 \times 8 \times 3 / 100 = 2400$. Total = ₹12,400.

Compound interest: interest on interest#

With compound interest, each year's interest is added to the principal, and next year's interest is calculated on the bigger amount.

Example: ₹10,000 at 8% compounded yearly for 3 years:

Compound interest earns ₹197.12 more than simple interest here. The gap looks small for 3 years, but it grows dramatically with time.

Compounding more often#

If interest is added half-yearly or quarterly, divide the rate and multiply the periods:

where $n$ is the number of times per year (2 for half-yearly, 4 for quarterly).

Example: ₹10,000 at 8% for 1 year compounded half-yearly: $A = 10000 \times (1.04)^2 = 10816$. That is ₹16 more than yearly compounding.

The Rule of 72: a quick mental shortcut#

To estimate how long money takes to double, divide 72 by the yearly rate:

Why starting early matters#

Imagine two friends who each save at 8% a year compounded yearly:

• Asha saves ₹1,000 a month from age 22 to 32 (10 years), then stops but leaves the money invested.
• Ravi starts at 32 and saves ₹1,000 a month until 42 (also 10 years).

At age 42, Asha's money has had 10 extra years to compound, so her total is roughly double Ravi's, even though both put in the same ₹1,20,000. Time is the most powerful part of the formula, because it sits in the exponent.

Practice questions#

1. Find the compound interest on ₹5,000 at 10% per year for 2 years.
2. At what rate will ₹8,000 become ₹9,680 in 2 years at compound interest?
3. Using the Rule of 72, how long will money take to double at 9%?

Answers:

1. $A = 5000 \times 1.1^2 = 6050$, so CI = ₹1,050.
2. $9680/8000 = 1.21 = 1.1^2$, so the rate is 10% per year.
3. 72 ÷ 9 = about 8 years.