Compound Interest Formula With Examples
The compound interest formula is A = P(1 + r/n)^(nt), where P is the principal, r is the annual interest rate as a decimal, n is the number of times interest compounds per year, and t is the number of years. More frequent compounding (monthly instead of yearly, for example) gives a slightly higher final amount for the same annual rate.
The compound interest formula is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal you start with, r is the annual interest rate written as a decimal, n is how many times interest compounds each year, and t is the number of years the money grows. Increasing n while keeping the annual rate the same gives a slightly larger final amount, because interest itself starts earning interest more often.
Breaking down each part of the formula
- P (Principal): the amount you start with, before any interest is added.
- r (Rate): the annual interest rate, written as a decimal. An 8% annual rate is r = 0.08.
- n (Compounding frequency): how many times per year interest is calculated and added. Yearly compounding is n = 1, quarterly is n = 4, monthly is n = 12.
- t (Time): the number of years the money is invested or borrowed for.
- A (Amount): the total value at the end, principal plus all the compounded interest.
The interest earned alone is simply A minus P, once you have worked out A from the formula.
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Worked example 1: a student's yearly savings
Assume a student deposits Rs 50,000 into an account offering 6% annual interest, compounded yearly, for 3 years, with no further deposits.
| Variable | Value |
|---|---|
| P (Principal) | Rs 50,000 |
| r (Rate) | 0.06 (6%) |
| n (Compounding) | 1 (yearly) |
| t (Time) | 3 years |
A = 50,000 x (1 + 0.06/1)^(1x3) = 50,000 x (1.06)^3 = 50,000 x 1.191016 = Rs 59,551 (rounded). The interest earned over 3 years is about Rs 9,551, on top of the original Rs 50,000.
Worked example 2: monthly compounding on a larger sum
Assume an investor puts in Rs 2,00,000 at an assumed 8% annual return, compounded monthly, for 5 years, with no additional deposits.
| Variable | Value |
|---|---|
| P (Principal) | Rs 2,00,000 |
| r (Rate) | 0.08 (8%, assumed) |
| n (Compounding) | 12 (monthly) |
| t (Time) | 5 years |
A = 2,00,000 x (1 + 0.08/12)^(12x5) = 2,00,000 x (1.006667)^60, which works out to about Rs 2,97,969, or roughly Rs 2,98,000. That is roughly Rs 98,000 of interest over 5 years, more than the same rate would earn if compounded only yearly (about Rs 2,93,866), purely because of the monthly compounding frequency.
The difference between yearly and monthly compounding at the same stated annual rate is real but modest: about Rs 4,100 over 5 years on Rs 2,00,000 at 8% in example 2, around 1.4% of the final amount, not a dramatic jump. It grows more noticeable with a higher rate, a longer time period, or a much larger principal.
Compound interest versus simple interest
Simple interest only ever applies to the original principal, so it grows in a straight line year after year. Compound interest applies to the principal plus all previously earned interest, so it grows faster the longer the money stays invested, since each period's interest becomes part of the base for the next period's calculation. Over a short period the difference is small, but over 10 or 20 years, compound interest can produce a noticeably larger final amount than simple interest at the same stated rate.
Where you will see this formula in real life
- Fixed deposits and recurring deposits, where banks state a compounding frequency (usually quarterly).
- Savings account interest, often compounded quarterly or monthly depending on the bank.
- Loan interest, where the same formula (from the lender's side) determines how much a borrowed amount grows if unpaid.
- Long-term investment projections, though real investments like mutual funds do not guarantee a fixed rate the way this formula assumes.
Why the exponent (nt) matters more than it looks
The nt in the exponent is where most of compound interest's long-term power comes from: it is not just the number of years, but the number of years multiplied by how many times per year compounding happens. Doubling the number of years doubles nt directly, but since the formula raises (1 + r/n) to the power of nt, the final amount does not simply double along with it, it grows faster than that. This is why financial explanations often say compound interest "accelerates" over time: the growth curve gets steeper the longer the money is left untouched, rather than climbing at a constant slope like simple interest does.
A practical way to see this without redoing the full calculation each time is to compare the same principal and rate at two different values of t, say 5 years and 10 years, using a calculator. The jump from year 5 to year 10 is noticeably larger than the jump from year 0 to year 5, even though both spans cover the same five years, precisely because of this compounding effect.
Common mistakes when using the compound interest formula
- Forgetting to convert a percentage rate to a decimal before plugging it into the formula (8% is 0.08, not 8).
- Using the wrong value for n; quarterly is 4, not 3, and monthly is 12, not 1.
- Mixing up t in years with t in months without adjusting n and t consistently.
- Treating an assumed investment return as guaranteed; real market-linked returns vary and are not fixed like a bank's stated interest rate.
This article uses assumed rates for illustration only and is not investment advice. Confirm actual rates with your bank or a financial professional before making a decision. For a different kind of growth calculation on investments with ups and downs, the CAGR calculator is more appropriate than this formula, since it does not assume a fixed periodic rate. For a fixed-rate product with a stated compounding frequency, check it with the FD calculator.
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Frequently asked questions
What is the compound interest formula?
A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual rate as a decimal, n is how many times interest compounds per year, and t is the number of years.
Does more frequent compounding always mean much more interest?
It means somewhat more interest for the same stated annual rate, but the difference between, say, yearly and monthly compounding is usually modest unless the rate is high, the time period is long, or the principal is large.
What is the difference between compound interest and simple interest?
Simple interest is calculated only on the original principal every period, so it grows in a straight line. Compound interest is calculated on the principal plus all previously earned interest, so it grows faster the longer the money stays invested.
How do I convert a percentage rate for the formula?
Divide the percentage by 100 to get a decimal. An 8% rate becomes r = 0.08, and a 6.5% rate becomes r = 0.065.
Can I use this formula for a loan instead of savings?
Yes, the same formula shows how a borrowed amount would grow if left completely unpaid, though most real loans also involve regular repayments, which change the calculation. Use an EMI calculator for a loan with monthly repayments.
Sources
- Khan Academy, Introduction to compound interest (checked 2026-09)
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