Albert Einstein is often (probably wrongly) credited with calling compound interest the eighth wonder of the world – but the maths behind the quote is real. Compound interest is interest earned on interest, and over long periods it turns small, regular savings into large sums. This guide explains the compound interest formula, shows how to calculate compound interest step by step, compares compound interest vs simple interest, and explains why the compounding frequency and the number of years matter so much.
What Is Compound Interest?
With simple interest, you earn interest only on the money you originally invested (the principal). With compound interest, the interest you earn is added to your balance, and in the next period you earn interest on that bigger balance too. The longer this continues, the faster the balance grows – the growth curve bends upwards over time.
The Compound Interest Formula
A = P × (1 + r ÷ n)n × t
- A = amount at maturity (principal + interest)
- P = principal, the amount you invest
- r = annual interest rate as a decimal (8% = 0.08)
- n = number of times interest is compounded per year (1 yearly, 4 quarterly, 12 monthly)
- t = time in years
Compound interest = A − P
How to Calculate Compound Interest: Step-by-Step Example
Suppose you invest ₹1,00,000 at 8% a year for 10 years, compounded yearly.
- P = 1,00,000; r = 0.08; n = 1; t = 10
- 1 + r ÷ n = 1.08
- (1.08)10 ≈ 2.1589
- A = 1,00,000 × 2.1589 = ₹2,15,892
- Compound interest = 2,15,892 − 1,00,000 = ₹1,15,892
Your money has more than doubled. With simple interest at the same 8% for 10 years, you would earn only ₹80,000 of interest, ending with ₹1,80,000.
Compounding Frequency: Yearly vs Quarterly vs Monthly
The more often interest is added, the faster your money grows, because interest starts earning interest sooner. Here is the same ₹1,00,000 at 8% for 10 years with different compounding frequency:
| Compounding | n | Maturity value | Interest earned |
|---|---|---|---|
| Yearly | 1 | ₹2,15,892 | ₹1,15,892 |
| Half-yearly | 2 | ₹2,19,112 | ₹1,19,112 |
| Quarterly | 4 | ₹2,20,804 | ₹1,20,804 |
| Monthly | 12 | ₹2,21,964 | ₹1,21,964 |
| Continuous | ∞ | ₹2,22,554 | ₹1,22,554 |
Quarterly compounding is what most Indian banks use for fixed deposits, and PPF compounds yearly. The difference between monthly and continuous compounding is tiny, which shows there is a limit to how much frequency can help – the rate and time matter far more.
Compound Interest vs Simple Interest
Simple interest = P × r × t
| ₹1,00,000 at 8% | Simple interest total | Compound (yearly) total | Extra from compounding |
|---|---|---|---|
| 5 years | ₹1,40,000 | ₹1,46,933 | ₹6,933 |
| 10 years | ₹1,80,000 | ₹2,15,892 | ₹35,892 |
| 20 years | ₹2,60,000 | ₹4,66,096 | ₹2,06,096 |
Over 5 years the gap is small. Over 20 years compounding earns about 2.3 times as much interest as simple interest (₹3,66,096 against ₹1,60,000). This is the power of compounding: the gap between the two grows every single year.
Compound Interest Table: ₹10,000 at Different Rates
This table shows what a one-time investment of ₹10,000 grows to with yearly compounding. Compare the columns to see how the rate and the time period interact:
| Rate | 5 years | 10 years | 20 years | 30 years |
|---|---|---|---|---|
| 6% | ₹13,382 | ₹17,908 | ₹32,071 | ₹57,435 |
| 8% | ₹14,693 | ₹21,589 | ₹46,610 | ₹1,00,627 |
| 10% | ₹16,105 | ₹25,937 | ₹67,275 | ₹1,74,494 |
| 12% | ₹17,623 | ₹31,058 | ₹96,463 | ₹2,99,599 |
Over 30 years, 12% turns ₹10,000 into almost ₹3 lakh, while 6% gives about ₹57,000. A difference of a few percentage points becomes enormous when it compounds for decades – which is why small differences in fund costs and interest rates matter so much for long-term savers.
Compound Interest and Inflation: Your Real Return
Inflation compounds too. If your money earns 8% while prices rise 6% a year, your real return is only about 1.89% a year, calculated as (1.08 ÷ 1.06) − 1. After 20 years, ₹1,00,000 grows to ₹4,66,096 in rupees, but in today's buying power that is worth only about ₹1,45,331. Always compare returns with inflation, and remember that tax on interest reduces the real return further. Investments that beat inflation after tax are the ones that genuinely grow your wealth.
The Rule of 72: How Long to Double Your Money
A quick mental shortcut is the Rule of 72: divide 72 by the annual interest rate to estimate how many years it takes to double your money.
- At 8%: 72 ÷ 8 = 9 years (the exact answer is 9.01 years).
- At 12%: 72 ÷ 12 = 6 years (exact: 6.12 years).
- At 6%: 72 ÷ 6 = 12 years.
The rule works best for rates between about 6% and 10%. It also works in reverse: at 6% inflation, prices double roughly every 12 years.
Compound Interest on Monthly Investments
The formula above is for a one-time lump sum. When you invest every month – through a SIP, recurring deposit or EPF – each instalment compounds for a different length of time. The future value of a series of monthly payments is:
FV = M × [(1 + i)n − 1] ÷ i × (1 + i)
where M is the monthly amount, i is the monthly rate and n is the number of months. For example, ₹10,000 a month at 12% for 20 years grows to about ₹1 crore (₹99,91,479) from ₹24 lakh invested. Try it in our SIP calculator.
Where Compound Interest Works For and Against You
Working for you
- Fixed deposits – interest compounds quarterly in most banks. Check yours with the FD calculator.
- PPF and EPF – interest is compounded yearly and is tax-free under the EEE rules. See the PPF calculator and EPF calculator.
- Mutual funds and shares – returns compound as gains are reinvested.
Working against you
- Credit card debt – unpaid balances can attract interest of 36%–48% a year, compounding monthly.
- Loans with missed payments – unpaid interest can be added to the balance.
- Inflation – rising prices compound too, steadily reducing what your money can buy.
Compound Interest in Excel
- Maturity value:
=P*(1+r/n)^(n*t), for example=100000*(1+8%/4)^(4*10)gives ₹2,20,804. - Using the FV function:
=FV(8%/4, 40, 0, -100000)gives the same result. - Monthly investments:
=FV(12%/12, 240, -10000, 0, 1)gives the value of a ₹10,000 monthly SIP after 20 years.
How to Make Compound Interest Work Harder
- Start early. Time is the most powerful input – 20 years of growth is worth far more than twice 10 years.
- Reinvest the interest instead of taking monthly or quarterly payouts.
- Choose more frequent compounding when the rates are the same.
- Increase your contribution each year as your income grows.
- Pay off high-interest debt first – compounding at 36% against you beats compounding at 8% for you.
Common Compound Interest Mistakes
- Using the annual rate with monthly periods. Divide the annual rate by the number of periods per year and multiply the years by the same number.
- Forgetting to subtract the principal. The formula gives the maturity amount; the interest is A − P.
- Comparing rates with different compounding. 8% compounded monthly is better than 8% compounded yearly – compare effective annual yields instead.
- Ignoring tax. FD interest is taxed every year, which reduces the amount that keeps compounding.
Frequently Asked Questions
What is the formula for compound interest?
A = P × (1 + r/n)^(n×t), where P is the principal, r the annual rate as a decimal, n the number of compounding periods per year and t the number of years. Compound interest is A − P.
How much is ₹1 lakh at 8% compound interest for 10 years?
About ₹2,15,892 with yearly compounding and ₹2,20,804 with quarterly compounding.
What is the difference between simple and compound interest?
Simple interest is earned only on the original principal. Compound interest is also earned on previously added interest, so it grows faster, especially over long periods.
Which is better: monthly or quarterly compounding?
At the same interest rate, monthly compounding gives slightly more than quarterly. On ₹1 lakh at 8% for 10 years the difference is about ₹1,160.
How long does it take to double money at 8%?
About 9 years, using the Rule of 72 (72 ÷ 8 = 9). The exact figure with yearly compounding is 9.01 years.
Do banks use compound interest on fixed deposits?
Yes. Most Indian banks compound FD interest quarterly for cumulative deposits.
What is the effective annual rate?
The effective annual rate is the true yearly return after compounding. At 8% compounded quarterly it is about 8.24%, because interest earned early in the year also earns interest. Use it to compare products with different compounding frequencies.
Is compound interest good or bad?
It is good when you are saving or investing, because your returns grow faster over time. It is bad when you owe money, such as on a credit card, because unpaid interest also attracts interest.
Note: Figures are rounded to the nearest rupee and ignore tax. Actual returns depend on the product, rate changes and taxation.