Compound Interest Calculator
Enter a principal, an annual interest rate, a term and how often interest is compounded to find the future value and the interest. It also shows the result with simple interest and the effective annual rate.
The compound interest formula
Future value = principal × (1 + annual rate ÷ n)^(n × years), where n is the number of times interest is compounded in a year.
Interest = future value − principal.
Compound interest vs. simple interest
- Simple interest: interest is earned on the principal only. Future value = principal × (1 + annual rate × years).
- Compound interest: interest is also earned on the interest added earlier. With the same rate, compound interest grows faster the longer the term.
Compounding frequency and the effective annual rate
The more often interest is compounded, the more interest you earn in a year at the same annual rate. The effective annual rate is the yearly growth that results from compounding, expressed as a rate: (1 + annual rate ÷ n)^n − 1.
Terms that do not give a whole number of compounding periods
This calculator only accepts a term for which n × term is a whole number of compounding periods. If the term ends in the middle of a compounding period, it shows an error, because there is no single standard way to treat a partial period.
| Compounding frequency | Terms that can be calculated |
|---|---|
| Annually (1 time a year) | A multiple of 12 months (whole years) |
| Semiannually (2 times a year) | A multiple of 6 months |
| Quarterly (4 times a year) | A multiple of 3 months |
| Monthly (12 times a year) | Any number of months |
| Daily (365 times a year) | A multiple of 12 months (whole years) |
For example, with daily compounding, a term of 6 months would be 365 × 6 ÷ 12 = 182.5 compounding periods, which is not a whole number, so it is not calculated. Daily compounding is a model of 365 compounding periods a year. It does not count the actual days between two dates (leap days are not included).
Rounding
The amounts are not rounded in each period. They are rounded once, at the end to 2 decimal places (round to nearest by default). Real financial products may round in every period or use other methods, so their results can differ slightly. This rounding rule is a choice made by this calculator.
Precision and rounding
- Calculation: the calculator uses exact fractions and whole numbers, not floating-point numbers. An amount with 2 decimal places is converted to a whole number of the smallest unit (for example, cents) before calculating, and the result is converted back. No rounding happens in the middle of the calculation.
- Rounding: the amounts shown are rounded once, at the end, to 2 decimal places, with the rule you choose (round down, round to nearest, round up; round to nearest rounds a value exactly halfway up). "Future value before rounding" is shown to 4 decimal places, so it is itself a rounded display.
- How the amounts relate: the interest is the rounded future value minus the principal. "Compound minus simple" is the difference between the two rounded amounts, so it can differ by 0.01 from rounding the exact difference. The effective annual rate and the ratio are rounded to 4 decimal places for display.
- What this means: there is no floating-point error, but every displayed amount is a rounded value (to 2 decimal places). Real products may round in every period, so their results can differ.
- Checked against an independent calculation: the results were compared with a separate calculation that multiplies period by period with whole numbers (about 1,500 cases, including a principal of 0.01, a rate of 0.0001%, the largest principal, and 1,200 monthly periods). All amounts matched exactly.
Limits
The principal can be up to 9,999,999,999.99. The annual rate is 0% to 100% (up to 4 decimal places), and the term is 1 month to 100 years (at most 36,500 compounding periods). If the future value has more than 13 digits before the decimal point, it is shown as "about m × 10^e" and the full digits are in a collapsible section.
Examples
| Input | Result |
|---|---|
| Principal 1,000,000, 3% a year, 10 years, compounded annually | Future value 1,343,916.38 (interest 343,916.38). With simple interest it is 1,300,000.00, a difference of 43,916.38 |
| The same, compounded monthly | Future value 1,349,353.55. The effective annual rate is about 3.0416% |
| Principal 5,000.00, 5% a year, 5 years, compounded quarterly | Future value 6,410.19 (interest 1,410.19). With simple interest: 6,250.00 |
| Principal 10,000.00, 6% a year, 3 years, compounded monthly | Future value 11,966.81 (interest 1,966.81) |
What this calculator does not do
It does not include taxes on interest, current interest rates, the terms of specific accounts, bonds, funds or loans, fees, inflation, regular deposits, continuous compounding, or solving for a target amount or a rate. To compare a value with another as a percentage, see the Percentage Change Calculator; for powers and logarithms, the Exponent & Logarithm Calculator.
Frequently asked questions
Which is larger, compound or simple interest?
When the rate is above 0% and the term is longer than one compounding period, compound interest is larger. When the term is exactly one compounding period, they are equal.
Will this match my bank or fund exactly?
Not necessarily. This is a mathematical value for the conditions you enter. Real products differ in rounding, taxes, fees and how interest is credited.
Can I enter the monthly rate?
Enter the annual rate. With monthly compounding, the calculator uses the annual rate ÷ 12 for each month.
Can I enter cents (or pence)?
Yes. The principal accepts up to 2 decimal places. The calculation uses whole numbers of the smallest unit (cents or pence), and the amounts are rounded once at the end to 2 decimal places.