In plain words: type your starting amount, the yearly interest rate and how long you will leave the money. The calculator shows what it could grow to when interest earns interest, how much of that is pure interest, and a year-by-year table so you can see growth speed up.
Last updated by Hira Science Academy. Educational tool; see the limitations section below.
What this compound interest calculator does
This free compound interest calculator estimates the future value of a single starting amount when interest is added to the balance at regular intervals. Enter the principal, the annual interest rate, the time period and how often interest compounds. You get the future value, the interest earned, the effective annual rate (APY), a comparison with simple interest and a year-by-year table. Because interest in later periods is earned on earlier interest, growth speeds up over time, which is why the same rate gives very different results over 10 and 30 years. If you also add money every month, use the savings calculator. To measure what an investment actually returned, use the ROI calculator. Debt compounds too: the loan repayment calculator shows what a borrowing costs, and the monthly budget calculator shows how much room you have to save.
How to use the compound interest calculator
- Enter the initial amount, the money you start with.
- Enter the annual interest rate as a percentage, such as 5 or 7.25.
- Enter the time period in years. Use decimals for part-years.
- Choose the compounding frequency: annually, semi-annually, quarterly, monthly or daily. If you do not know it, monthly is a common default for savings accounts.
- Press Calculate. Read the future value first, then open the year-by-year table to see how each year contributes.
- Use Copy answer to copy the result, or press an example chip to see a ready-made scenario.
The compound interest formula
What each symbol means
- \(A\) — future value
- The balance at the end, including the original amount and all interest.
- \(P\) — principal
- The amount you start with.
- \(r\) — annual rate as a decimal
- A 5% rate is \(r = 0.05\).
- \(n\) — compounding periods per year
- 1 for annual, 2 for semi-annual, 4 for quarterly, 12 for monthly and 365 for daily compounding.
- \(t\) — time in years
- The length of time the money stays invested.
Worked examples
Example 1: $10,000 at 5% for 10 years, compounded monthly
- Monthly rate: \(r/n = 0.05 / 12 = 1.004167\). Number of periods: \(nt = 12 \times 10 = 120\).
- Growth factor: \((1 + 0.05/12)^{120} = 1.6470\).
- Future value: \(10{,}000 \times 1.6470 \approx\) $16,470.09. Interest earned: $6,470.09.
- Effective annual rate (APY): about 5.116%, slightly above the 5% quoted rate because interest is added monthly.
Example 2: $5,000 at 7% for 20 years, compounded annually
- With annual compounding \(n = 1\), so the formula is \(A = 5{,}000 \times 1.07^{20}\).
- \(1.07^{20} \approx 3.8697\), so the balance is about $19,348.42.
- Interest earned: $14,348.42, nearly three times the original deposit.
Example 3: compound versus simple interest on $10,000 at 5% for 10 years
- Simple interest: \(10{,}000 \times (1 + 0.05 \times 10) = \) $15,000.00.
- Compound interest, compounded annually: \(10{,}000 \times 1.05^{10} = \) $16,288.95.
- Compounding adds $1,288.95 over the same ten years, and the gap widens every year.
Example 4: ₨500,000 at 12% for 5 years, compounded monthly
- Monthly rate: \(0.12 / 12 = 0.01\). Periods: \(12 \times 5 = 60\).
- Growth factor: \(1.01^{60} \approx 1.8167\).
- Future value: about ₨908,348.35, of which ₨408,348.35 is interest. Choose PKR in the currency list to try it.
How compounding frequency changes the result
The more often interest is added, the more often earlier interest starts earning interest of its own. The effect is real but modest compared with the effect of the rate or the time. The table below uses the same deposit, rate and period and changes only the frequency.
| Frequency | Future value | Interest earned |
|---|---|---|
| Annually | $16,288.95 | $6,288.95 |
| Semi-annually | $16,386.16 | $6,386.16 |
| Quarterly | $16,436.19 | $6,436.19 |
| Monthly | $16,470.09 | $6,470.09 |
| Daily (365) | $16,486.65 | $6,486.65 |
Moving from annual to daily compounding adds about $197.70 over ten years on a $10,000 deposit. Raising the rate by one percentage point or leaving the money for longer usually matters far more than the compounding schedule.
How time and rate affect growth
Compounding rewards patience. The table shows what $1,000 becomes with annual compounding at four different rates. Read across to see the effect of the rate and down to see the effect of time.
| Time | At 3% | At 5% | At 7% | At 9% |
|---|---|---|---|---|
| 10 years | $1,344 | $1,629 | $1,967 | $2,367 |
| 20 years | $1,806 | $2,653 | $3,870 | $5,604 |
| 30 years | $2,427 | $4,322 | $7,612 | $13,268 |
Illustrative arithmetic only. These are not forecasts and not product rates.
The Rule of 72: a quick doubling estimate
Divide 72 by the annual rate (as a percentage) to estimate how many years it takes money to double. At 6% the estimate is 12 years; the exact figure with annual compounding is 11.90 years. The rule is most accurate for rates between about 6% and 10%.
| Rate | Rule of 72 | Exact |
|---|---|---|
| 2% | 36.0 years | 35.0 years |
| 4% | 18.0 years | 17.7 years |
| 6% | 12.0 years | 11.9 years |
| 8% | 9.0 years | 9.0 years |
| 10% | 7.2 years | 7.3 years |
| 12% | 6.0 years | 6.1 years |
Interest rate, APR and APY: which number do I use?
- Nominal rate (APR)
- The stated yearly rate before the effect of compounding. Enter this in the calculator along with the compounding frequency.
- APY or AER
- The effective annual rate after compounding. US banks usually quote APY on deposit accounts; UK providers quote AER. At 5% compounded monthly the APY is 5.116%, and compounded daily it is 5.127%.
- Converting an APY to a nominal rate
- If you only know the APY, either enter it with annual compounding (frequency = 1), or use the nominal rate your provider also publishes.
The word APR is used differently on loans, where it usually includes some fees. For borrowing costs use the loan repayment calculator.
Where compound interest is used
- Savings and deposit accounts. Banks in the US, UK, Canada, Australia, Pakistan and elsewhere pay interest or profit on balances; check how often your provider adds it.
- Long-term investing. Reinvested returns compound. Real returns vary year to year, so treat a constant rate as a planning assumption, not a promise.
- Retirement and education funds. Tax-advantaged accounts such as an IRA in the US, an ISA in the UK or a TFSA in Canada follow their own rules and limits; this calculator ignores them.
- Debt. Credit cards and some loans compound against you. A small unpaid balance can grow quickly.
- Maths and science classes. Compound growth is an exponential function. The exponent and power calculator and the percentage calculator help you check each step by hand.
Common mistakes to avoid
- Entering 0.05 instead of 5. The rate field expects a percentage, so type 5 for 5%.
- Mixing up months and years. The time period is in years. Enter 18 months as 1.5.
- Ignoring inflation and tax. A nominal balance of $16,470 in ten years buys less than $16,470 does today, and interest may be taxable.
- Assuming a constant rate. Variable-rate accounts and market investments change over time.
- Forgetting fees. Account or fund fees reduce the effective rate. Subtract them from the rate for a more cautious estimate.
- Comparing a nominal rate with an APY. Compare like with like, or convert both to APY.
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Assumptions and limitations
- Constant rate. The rate stays the same for the whole period. Variable rates and market returns will differ.
- No deposits or withdrawals. Only the starting amount is modelled. For regular deposits use the savings calculator.
- No fees, tax or inflation. These reduce real-world results. Subtract expected fees from the rate for a cautious view.
- Rounding. Figures are shown to two decimal places. Banks may round at each compounding step, so their statements can differ by a few cents.
- Privacy. The maths runs in your browser. The numbers you type are not sent to a Hira Academy calculation server. Like the rest of the site, the page loads Google Analytics and advertising scripts; see the Privacy Policy.
Frequently asked questions about the Compound Interest Calculator
What is compound interest?
Compound interest is interest calculated on the original amount plus the interest already added. Each period the balance is larger, so the next interest payment is larger too. This is why growth accelerates over long periods.
How do you calculate compound interest?
Use A = P(1 + r/n)^(nt), where P is the starting amount, r is the annual rate as a decimal, n is how many times interest compounds per year and t is the number of years. Subtract P from A to get the interest. For example, $10,000 at 5% compounded monthly for 10 years grows to about $16,470.09.
What is the difference between simple and compound interest?
Simple interest is always calculated on the original principal. Compound interest is calculated on the principal plus accumulated interest. On $10,000 at 5% for 10 years, simple interest gives $15,000.00 while annual compounding gives $16,288.95.
How does compounding frequency affect my balance?
More frequent compounding gives slightly more interest at the same quoted rate. On $10,000 at 5% for 10 years the balance is $16,288.95 with annual compounding and $16,486.65 with daily compounding, a difference of about $197.70.
What is the difference between APR and APY?
APR is the nominal yearly rate. APY (called AER in the UK) is the effective yearly rate after compounding is included. A 5% rate compounded monthly has an APY of about 5.116%. Compare accounts using APY and compare loans using APR.
What is the Rule of 72?
The Rule of 72 estimates how long it takes money to double: divide 72 by the annual interest rate in percent. At 8% the estimate is 9 years. It is a quick mental shortcut, and the calculator gives the exact figure for your inputs.
Can I add regular deposits in this calculator?
This calculator models a single starting amount with no further deposits. To include monthly contributions, use the savings calculator.
How is the effective annual rate calculated?
APY = (1 + r/n)^n - 1. It tells you what the quoted rate is worth over a full year once compounding is included. The calculator shows it in the results for your chosen frequency.
Can I use this for loans or credit cards?
The same maths describes interest that grows against you. For a fixed loan with regular repayments, the loan repayment calculator gives the monthly payment and total interest, which is more useful than a single growth figure.
Does compound interest work the same in every country?
The mathematics is the same everywhere. Products differ: rates are quoted differently, some providers call the return a profit rate, and tax rules vary. Enter the rate and compounding schedule your own provider states.
Are the results guaranteed?
No. The calculator assumes a constant rate and no fees, taxes or withdrawals. Real accounts and investments can behave differently. Treat the figure as an estimate.
Is my data stored or sent anywhere?
No. The calculation runs in your browser. The values you type are not sent to a Hira Academy calculation server.
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