Compound Interest Explained: How Money Grows Over Time

When you save or lend money, you earn interest: a payment for letting someone else use it. There are two ways to work it out.

• Simple interest is calculated only on the original sum, called the principal. You earn the same amount every year.
• Compound interest is calculated on the principal plus all the interest already added. Each year’s interest joins the balance, so the next year’s interest is worked out on a bigger number.

In short, with compounding your interest starts earning interest of its own.

When interest is added once a year, the amount after n years is:

A = P × (1 + R/100)^n

Here A is the final amount, P is the principal, R is the yearly rate in per cent and n is the number of years. The compound interest itself is A − P.

Simple interest grows in a straight line instead: A = P × (1 + R × n/100). The two formulas give the same answer after one year, but the gap widens every year after that.

Suppose Meera, who lives in Pune, puts ₹1,00,000 into a scheme that pays an assumed fixed 8% a year, added once a year, and never withdraws it.

After	Simple interest	Compound interest
1 year	₹1,08,000	₹1,08,000
10 years	₹1,80,000	₹2,15,892
20 years	₹2,60,000	₹4,66,096
30 years	₹3,40,000	₹10,06,266

In the first year both methods pay the same ₹8,000. In year 30, the compound pot earns ₹74,538 in a single year, because 8% is now being worked out on a balance of more than ₹9 lakh. After 30 years, compounding has produced ₹6,66,266 more than simple interest from exactly the same deposit.

Because the growth builds on itself, time is the most powerful ingredient. Compare two friends who each invest ₹1,00,000 once, at the same assumed 8% a year, and both withdraw at age 55:

• Arjun invests at 25, so his money compounds for 30 years and reaches ₹10,06,266.
• Kavya invests at 35, so hers compounds for 20 years and reaches ₹4,66,096.

They put in the same amount, yet Arjun ends up with more than twice as much, simply because his money had ten extra years to grow. Most of the growth happens in the later years, which is why the curve on the chart bends upwards.

A quick way to estimate how long money takes to double is the Rule of 72: divide 72 by the yearly interest rate. At 8%, 72 ÷ 8 = 9, so money roughly doubles in 9 years. The exact answer is 9.01 years, so the shortcut is close, but it is only an estimate.

Interest can also be added more than once a year. At 8% a year compounded quarterly, 2% is added every three months, so ₹1,00,000 becomes ₹1,08,243 after one year instead of ₹1,08,000. The more often interest is added, the faster the balance grows, although the difference is small.

The examples here assume a fixed 8% every year to keep the maths clear. In reality, deposit rates change over time, and inflation reduces what your money can buy. Market-linked investments, such as equity mutual funds, do not pay a fixed rate at all: their value can rise or fall, and returns are not guaranteed. Compounding works on whatever return you actually get, including losses.

This page is for learning only and is not investment advice. For decisions about your own money, speak to a SEBI-registered investment adviser.