Compound Interest Explained: Formula and Examples

Compound interest is interest that earns interest. It is the reason a small amount left alone for a long time can grow far more than you might expect, and the reason a debt can grow faster than you expect. This guide gives the formula, shows how the compounding frequency changes the answer, and explains the Rule of 72.

What compound interest means

The US Consumer Financial Protection Bureau puts it this way: compound interest is when you earn interest on the money you have saved and on the interest you earn along the way. The St. Louis Fed's classroom lesson defines it as interest paid on the principal as well as on the interest earned previously.

The CFPB's example is easy to follow. Start with 1,000 at 5% a year, compounded once a year. After the first year you have 1,050. After the second year you have 1,102.50, not 1,100, because the second year's interest is worked out on 1,050. That extra 2.50 is interest on interest.

The formula

A = P × (1 + r / n)^(n × t)

• A is the amount at the end.
• P is the principal, the money you start with.
• r is the yearly rate as a decimal. 8% is 0.08.
• n is how many times a year interest is added.
• t is the number of years.

Our compound interest calculator does this sum for you and lists the balance at the end of every year, so you can see the growth speed up.

A worked example

Take ₹1,00,000 at 8% a year, with interest added once a year. After 10 years the amount is about ₹2,15,892, so the interest earned is about ₹1,15,892. After 20 years it is about ₹4,66,096. Doubling the time more than doubles the interest, because each year's interest is added to a bigger balance.

How often interest is added

Same ₹1,00,000, same 8% a year, same 10 years. Only the number of times interest is added changes:

• Yearly: about ₹2,15,892
• Half-yearly: about ₹2,19,112
• Quarterly: about ₹2,20,804
• Monthly: about ₹2,21,964
• Daily: about ₹2,22,535

The CFPB lists compounding more often as one of the ways to help savings grow faster, and the numbers show why. Notice how small the steps get, though. Going from yearly to quarterly adds about ₹4,900. Going from monthly to daily adds about ₹570. The rate and the time matter far more than the frequency.

Check the terms of any deposit or loan you are looking at. How often interest is added is part of the offer, and it is not the same everywhere.

The Rule of 72

The St. Louis Fed lesson describes the Rule of 72 as a rule of thumb for estimating how long money takes to double. Divide 72 by the yearly interest rate, as a percentage, and you get the approximate number of years. The lesson's examples: at 4%, about 18 years; at 6%, about 12; at 9%, about 8; at 12%, about 6.

It is a quick estimate, not an exact answer. At 12% the exact doubling time is a little over 6 years, so ₹1 grows to about ₹1.97 in 6 years rather than exactly ₹2. For planning, that is close enough, and you can use the calculator when you want the exact figure.

Compound interest works against borrowers too

The same arithmetic applies when you owe money. If interest on a loan or card balance is added to what you owe and the next interest is charged on the larger amount, the debt grows the same way savings do. This is why paying off high-interest balances early matters.

Common mistakes

• Mixing up the rate and the period. A rate of 8% a year is not 8% a month.
• Forgetting that the result is only as good as the rate you assume, especially for investments whose returns go up and down. Compound interest on a fixed deposit is stated in advance. Returns on market investments are not.
• Ignoring tax and charges, which are not in the formula and reduce what you keep.
• Expecting a big difference from the compounding frequency alone.

How to use the calculator

Enter the principal, the yearly rate, the number of years and how often interest is added. Read the final amount, and then look at the year-by-year table to see how the interest grows. Try changing only one number at a time to see what matters most.

Sources

• How does compound interest work? (Consumer Financial Protection Bureau)
• Lesson 6B: Simple and Compound Interest (Federal Reserve Bank of St. Louis and Minnesota Council on Economic Education)