What Is Compound Interest? The Formula, Explained

Compound interest is interest you earn not only on your original money but also on the interest that money has already earned. That second layer - interest on interest - is what makes savings, fixed deposits and long-term investments grow faster the longer you leave them alone. This guide explains what compound interest is, how it differs from simple interest, and the standard formula A = P(1 + r/n)^(nt). It walks through a worked example with real numbers, shows why compounding frequency matters, covers the Rule of 72 shortcut for doubling your money, and points out where compounding helps you - and where it works against you.

Compound interest vs simple interest

The cleanest way to understand compounding is to compare it with simple interest. Simple interest is calculated only on the original amount you deposit or borrow, called the principal. The formula is I = P x r x t, where P is the principal, r is the annual rate as a decimal and t is the number of years. The principal never changes, so you earn the same amount every year.

Compound interest is different. After each period, the interest you earned is added to the principal, and the next period's interest is calculated on this larger balance. So the base keeps growing, and your interest grows with it. Over one or two years the gap is small, but over a decade or more it becomes large.

• Simple interest: earned on the original principal only, so the yearly amount is flat.
• Compound interest: earned on principal plus all previously accumulated interest, so it speeds up over time.
• On a loan or credit card, the same effect works against you - unpaid interest gets added to what you owe.

The compound interest formula

The standard formula for the final amount under compounding is:

A = P(1 + r/n)^(nt)

Where:

• A is the final amount, also called the maturity value - what you end up with.
• P is the principal - the amount you start with.
• r is the annual interest rate written as a decimal, so 8% becomes 0.08.
• n is the number of times interest is compounded per year (1 for annually, 4 for quarterly, 12 for monthly).
• t is the time in years.

The interest you actually earn is simply the final amount minus what you put in: compound interest = A - P. You never need to compute the powers by hand - the Compound Interest Calculator does it instantly - but knowing each part helps you see what is driving the result.

A worked example

Suppose you deposit 1,00,000 at 8% annual interest for 10 years, compounded once a year. Here P = 1,00,000, r = 0.08, n = 1 and t = 10.

1. Work out 1 + r/n = 1 + 0.08/1 = 1.08.
2. Raise it to the power nt = 1 x 10 = 10, so 1.08^10 = 2.158925.
3. Multiply by the principal: A = 1,00,000 x 2.158925, which is about 2,15,892.
4. Subtract the principal to get the interest: 2,15,892 - 1,00,000 = about 1,15,892.

So your 1,00,000 more than doubles, and the interest earned (about 1,15,892) is larger than the original deposit. With simple interest at the same 8% for 10 years you would earn only 1,00,000 x 0.08 x 10 = 80,000. The extra 35,892 is the value compounding adds - interest that itself earned interest.

How compounding frequency matters

The n in the formula is how often interest is added during the year. At the same nominal annual rate, compounding more often gives a slightly higher final amount, because interest starts earning interest sooner. Using the same 1,00,000 at 8% for 10 years:

• Compounded annually (n = 1): A is about 2,15,892.
• Compounded quarterly (n = 4): A is about 2,20,804.
• Compounded monthly (n = 12): A is about 2,21,964.

Moving from annual to monthly compounding adds about 6,072 over the decade on the same headline rate. The difference is real but modest, and it shrinks as the rate falls. This is why it pays to check not just the advertised rate but how often interest is compounded when comparing two deposits.

The power of time and the Rule of 72

Time is the strongest force in compounding. Because each year's growth builds on a bigger base, the curve gets steeper the longer you wait, and most of the gains in a long investment come in the final years. A quick mental shortcut for this is the Rule of 72: divide 72 by the annual interest rate (written as a percent) to estimate how many years it takes your money to double.

At 8%, that is 72 / 8 = about 9 years to double. At 6% it is 72 / 6 = 12 years; at 12% it is 72 / 12 = 6 years. The rule is an approximation, not an exact figure, but it is close enough for fast comparisons and shows why even a couple of extra percentage points - or a few extra years - can make a big difference to the end result.

Where compound interest shows up

Compounding is everywhere in personal finance, working both for you and against you. It is worth recognising which side you are on.

• Savings accounts and fixed deposits, where interest is added periodically and grows on itself - see the FD Calculator.
• Mutual funds and equity investments, where reinvested returns compound over years; a regular plan is modelled in the SIP Calculator.
• Loans, credit cards and EMIs, where unpaid interest is added to your balance - here compounding increases what you owe, so carrying a credit-card balance is expensive.

The lesson is simple: let compounding run for you by investing early and staying invested, and avoid letting it run against you by clearing high-interest debt quickly.

Try it yourself

The fastest way to build intuition is to change the numbers and watch the result move. Enter a principal, a rate, a number of years and a compounding frequency in the Compound Interest Calculator, and see how much of your final amount comes from growth rather than your own deposit - then try stretching the time period to feel just how much later years contribute.