Compound interest explained: the formula, compounding frequency and the calculator

Albert Einstein is often quoted as calling compound interest the eighth wonder of the world. There is no proof that he said it, but the point behind the story is true: interest that earns interest grows in a way that surprises people. A small amount left alone for a long time can become a large one, and a debt that is not repaid grows just as quickly against you. The free Compound Interest Calculator shows how a lump sum grows with yearly, half-yearly, quarterly, monthly or daily compounding, next to what simple interest would give. This guide explains the formula, the effect of compounding frequency and how to compare offers fairly.

Simple and compound interest

Simple interest is calculated only on the original amount. If you deposit ₹1,00,000 at 10% a year, you earn ₹10,000 every year, no matter how long you wait. After 5 years the interest is ₹50,000 and the total is ₹1,50,000.

Compound interest is calculated on the original amount and on the interest already added. In year one you earn ₹10,000. In year two you earn 10% of ₹1,10,000, which is ₹11,000. In year three, 10% of ₹1,21,000, which is ₹12,100. The extra interest on interest is the whole difference. After 5 years the total is ₹1,61,051, so compounding earned ₹11,051 more than simple interest from the same deposit at the same rate.

Over a short time the gap is small. Over a long time it is enormous. At 12% for 20 years, ₹1,00,000 grows to ₹9,64,629 with yearly compounding, while simple interest would give ₹3,40,000 in total. Compounding earns about six times more interest.

The formula

A = P × (1 + r ÷ n)^(n × t)

• A is the final amount.
• P is the starting amount (the principal).
• r is the yearly rate as a decimal (10% is 0.10).
• n is how many times a year interest is added to the balance.
• t is the time in years.

The interest earned is A − P. For the example above, P = 1,00,000, r = 0.10, n = 1 and t = 5, so A = 1,00,000 × 1.1⁵ = ₹1,61,051. Simple interest uses a simpler formula: P × r × t.

Compounding frequency

The number n is how often the bank adds interest to your balance. More frequent compounding means interest starts earning interest sooner. The calculator offers five choices. For ₹1,00,000 at 8% for 5 years:

Compounding	Final amount	Effective yearly rate
Yearly	₹1,46,933	8.000%
Half-yearly	₹1,48,024	8.160%
Quarterly	₹1,48,595	8.243%
Monthly	₹1,48,985	8.300%
Daily	₹1,49,176	8.328%

Moving from yearly to daily compounding adds about ₹2,243 over five years. That is a real but modest gain. The rate and the time matter much more than the frequency: a deposit at 9% compounded yearly beats one at 8% compounded daily.

Effective yearly rate

The last column shows the effective annual rate: the single yearly percentage that would give the same result as the stated rate with its compounding. It is calculated as (1 + r ÷ n)ⁿ − 1. A deposit quoted at "8% compounded quarterly" really grows by 8.243% a year.

This number lets you compare offers fairly. Two banks may advertise the same 8%, but if one compounds quarterly and the other yearly, the first pays more. Convert both to the effective rate and the comparison is clear. The tool shows the effective rate with every result.

In India, many banks compound fixed-deposit interest quarterly, but terms vary by bank and by type of deposit, so choose the option in the calculator that matches your deposit's terms.

Using the calculator

1. Open the Compound Interest Calculator.
2. Enter the amount, the yearly interest rate and the number of years.
3. Choose the compounding frequency.
4. Read the maturity amount, the interest earned, the interest simple interest would have given, and the effective yearly rate.
5. Check the year-by-year table, where you can see both lines grow apart.

It all runs in your browser, so nothing you enter is stored.

The rule of 72

For a quick mental estimate of doubling time, divide 72 by the yearly rate in percent. At 9%, money doubles in about 72 ÷ 9 = 8 years. Check: ₹1,00,000 at 9% compounded yearly for 8 years becomes ₹1,99,256, which is very close to double. The rule works best for rates between about 6% and 12%. It is a shortcut, not an exact formula.

Compounding works against borrowers too

The same mathematics makes debt expensive. A credit-card balance that charges 3% a month compounds monthly, which is an effective rate of about 42.6% a year. If you pay nothing, the balance grows faster each month. That is why a small unpaid balance on a high-rate card becomes a big one. If you repay a loan monthly, use the EMI Calculator, which accounts for repayments. The compound interest calculator shows what happens when nothing is repaid.

Where compounding appears

• Fixed deposits. A cumulative FD adds interest to the deposit. The FD & RD Calculator uses quarterly compounding.
• Savings accounts. Interest is typically calculated daily on the balance and credited periodically.
• Mutual funds and shares. Returns are not fixed, but reinvested gains compound. The SIP Calculator shows a monthly investing plan.
• Provident funds and bonds. Many are compounded on a fixed schedule.
• Inflation. Prices compound too: 6% inflation halves the buying power of money in about 12 years.

What the calculator does not include

• Tax. Interest on deposits is generally taxable and TDS may be deducted, so your take-home amount is lower than the maturity value. The Income Tax Calculator can help you estimate the tax on income.
• Inflation. A larger number later is not the same as more purchasing power.
• Fees and penalties for early withdrawal.
• Variable rates. Real rates can change during the period.

Common mistakes

• Comparing stated rates without looking at the compounding.
• Forgetting that interest earned in early years drives the later years, so withdrawing it breaks the compounding.
• Assuming a bank's maturity value matches exactly. Banks round and count days slightly differently.
• Believing that a higher frequency beats a higher rate.
• Mixing months and years in the time field.

Quick answers

What is the difference between simple and compound interest? Simple interest is paid on the original amount only. Compound interest is paid on the amount plus the interest already earned.

Which compounding is best? More frequent is slightly better for savers and worse for borrowers, but the rate and time matter much more.

What is the effective rate? The yearly percentage that gives the same result as the stated rate with its compounding.

Does it work for loans? It shows how a debt grows if nothing is repaid. For monthly repayments use the EMI Calculator.

Is the calculation stored? No. It runs in your browser.