How compound interest is calculated
Compound interest is interest earned on your deposits and on interest already added to the balance. The SEC's investor education site defines it the same way. Each time interest is credited, the next period's interest is calculated on a larger balance.
- P
- Initial deposit
- r
- Nominal annual rate (5% → 0.05)
- n
- Compounding periods per year (12 for monthly, 365 for daily)
- t
- Years
Regular contributions are handled with the rate for each contribution period. When you contribute monthly but interest compounds daily or quarterly, the calculator converts the rate so both match:
FV = C × ((1 + i)m − 1) ÷ i (× (1 + i) if added at the start of each period)
- C
- Contribution each period
- p
- Contributions per year (12 or 1)
- i
- Rate per contribution period
- m
- Number of contributions (p × t)
The total is the growth of the initial deposit plus the growth of all contributions. At a 0% rate the balance is simply everything you put in.
Worked example
These are the calculator's defaults: $10,000 to start, $200 added at the end of every month, 5% compounded monthly, for 20 years.
| Initial deposit after growth$10,000 × (1 + 0.05/12)^240 | $27,126.40 |
|---|---|
| Monthly contributions after growth240 deposits of $200 | $82,206.74 |
| Estimated future balance | $109,333.14 |
| Total deposited | $58,000 |
| Interest earned | $51,333.14 |
Interest makes up about 47% of the final balance. Adding each contribution at the start of the month instead raises the result slightly, to $109,675.66, because every deposit earns one more month of interest.
APR, APY and compounding frequency
A quoted interest rate is usually a nominal annual rate. The annual percentage yield (APY) shows what you actually earn in a year once compounding is included. In the US, Regulation DD defines APY on the basis of the rate and compounding over a 365-day year. Its Appendix A gives the formula: APY = 100 × [(1 + interest ÷ principal)365/days − 1]. This calculator reproduces the appendix's first example ($61.68 of interest on $1,000 in a year → 6.17%) in its tests.
| Annually compounding | APY 5% · $10,500 |
|---|---|
| Quarterly compounding | APY 5.09% · $10,509.45 |
| Monthly compounding | APY 5.12% · $10,511.62 |
| Daily compounding | APY 5.13% · $10,512.67 |
More frequent compounding helps, but by less than many people expect. Going from monthly to daily compounding raises the APY by 0.01 percentage points at this rate. The rate itself and the time you leave the money invested matter far more. In the UK, savings rates are often shown as an AER (annual equivalent rate), which expresses the same idea as APY.
How to read your results
Time is the biggest lever. With the same deposits and rate, the balance grows like this:
| 10 years | $47,526.55 · $13,526.55 interest |
|---|---|
| 20 years | $109,333.14 · $51,333.14 interest |
| 30 years | $211,129.17 · $129,129.17 interest |
The well-known rule of 72 estimates how long money takes to double: 72 ÷ the rate. At 5% that gives 14.4 years. The exact figure for a single deposit compounded monthly is 13.9 years, so the rule is a quick approximation, not a formula.
The same mathematics works against you on debt. Interest charged on unpaid interest is why paying down high-rate balances early saves so much. See the early loan payoff calculator.
Assumptions
- The interest rate stays the same for the whole period.
- Interest compounds at the chosen frequency; daily compounding uses a 365-day year. Contributions use the equivalent rate for their own period, i = (1 + r/n)n/p − 1.
- Contributions are the same every period and are added at the start or end of each period, as you choose.
- No withdrawals, taxes, fees or inflation. Balances are not rounded until the result is shown.
- The APY is rounded to two decimal places, as Regulation DD requires for disclosures.
Limitations
- Investment returns are not fixed. A stock or fund portfolio can lose value, and an average return does not arrive evenly each year. Treat the rate as an assumption, not a promise.
- Banks credit interest in whole cents and may use daily balances, so statements can differ slightly from this estimate.
- Taxes on interest and investment gains, and the effect of inflation on what the money will buy, are not included. Both depend on where you live.
- Changing contributions, irregular deposits and withdrawals are not modeled.
Frequently asked questions
Is daily compounding much better than monthly?
Only slightly. At 5%, monthly compounding gives an APY of 5.12% and daily compounding 5.13%. A higher rate or more time has a much bigger effect than the compounding frequency.
What is the difference between APR and APY?
APR is a nominal yearly rate, typically quoted for borrowing. APY includes the effect of compounding over a year and is quoted for savings. For the same nominal rate, the APY is equal to or higher than the APR.
Should contributions be added at the start or the end of the period?
Choose what matches your plan. If you save at the beginning of each month, choose “start of period”: each deposit earns interest for one extra month. Payroll savings usually arrive during or at the end of the month, so “end of period” is the more conservative estimate.
Does the calculator include taxes and inflation?
No. Interest and investment gains may be taxed, and inflation reduces what the final balance can buy. Because both depend on your country and situation, the calculator shows the nominal result before them.
Sources
Definitions and rules referenced on this page. Calcendium is not affiliated with these publishers.
- Compound interest — glossary
U.S. Securities and Exchange Commission, Investor.gov · United States · Checked October 23, 2026
Definition of compound interest: interest earned on principal and on interest already added.
- Compound Interest Calculator
U.S. Securities and Exchange Commission, Investor.gov · United States · Checked October 23, 2026
The inputs a compound interest estimate depends on, including compounding frequency.
- Regulation DD, 12 CFR § 1030.2 — Definitions (annual percentage yield)
Consumer Financial Protection Bureau · United States · Checked October 23, 2026
Annual percentage yield reflects the interest rate and compounding over a 365-day period.
- Regulation DD, Appendix A to Part 1030 — Annual Percentage Yield Calculation
Consumer Financial Protection Bureau · United States · Checked October 23, 2026
The APY formula and its worked example used to test this calculator.