Compound Interest Calculator
Calculate future value, total contributions, compound growth, and effective annual rate across flexible time periods. Compare compounding frequencies, model beginning- or end-of-period contributions, and inspect a year-by-year growth schedule.
Additional
How to use the compound interest calculator
Enter the amount you are starting with, then add a recurring contribution if you plan to keep adding money. Contributions can be weekly, every two weeks, monthly, quarterly, every six months, or yearly.
Enter the annual rate and the length of the projection in years and months. Nominal rate is the default; choose how often that rate compounds.
Open Additional when you need an effective annual rate instead, or when contributions are made at the beginning rather than the end of each contribution period.
The result shows the projected ending balance, total contributions, compound growth, effective annual rate, and a detailed growth schedule.
What compound interest actually changes
Compound interest applies growth not only to the original principal but also to interest already added to the balance.
Suppose $1,000 earns 5% once a year. After the first year the balance is $1,050. In the second year, the 5% calculation is applied to $1,050 rather than only to the original $1,000.
Recurring contributions add another source of growth. Each contribution enters the balance at a different point in time, so earlier contributions generally have more time to compound than later ones.
Nominal rate and effective annual rate are not the same
A nominal annual rate states an annualized rate before the complete effect of within-year compounding. At a 12% nominal rate compounded monthly, for example, the periodic rate is 1% per month.
The effective annual rate measures the actual one-year percentage change after those compounding periods are applied. A 12% nominal rate compounded monthly produces an effective annual rate of about 12.6825%.
If your source already gives an effective annual rate, select Effective annual rate. The calculator then treats that percentage as the full one-year growth rate and does not apply a second compounding adjustment.
| Rate type | What it represents | Compounding frequency | When to use it |
|---|---|---|---|
| Nominal annual rate | Annualized stated rate before the full effect of compounding | Required | Use when you know the stated annual rate and how often it compounds |
| Effective annual rate | Actual one-year growth rate after compounding | Already included | Use when the annual rate already reflects the full compounding effect |
Compounding frequency changes the effective return
With the same positive nominal annual rate, more frequent compounding credits growth sooner. That raises the effective annual rate, although the incremental difference becomes smaller as compounding becomes increasingly frequent.
At a 12% nominal rate with no additional contributions, $1,000 becomes $1,120 after one year with annual compounding, about $1,126.83 with monthly compounding, about $1,127.47 with daily compounding, and about $1,127.50 with continuous compounding.
Continuous compounding is the limiting mathematical case. Instead of dividing the year into a fixed number of compounding periods, it uses exponential growth.
| Compounding | Modeled periods | How it is applied |
|---|---|---|
| Yearly | 1 per year | Interest compounds once each modeled year |
| Semi-annually | 2 per year | The nominal annual rate is divided across two periods |
| Quarterly | 4 per year | The nominal annual rate is divided across four periods |
| Monthly | 12 per year | The nominal annual rate is divided across twelve periods |
| Weekly | 52 per year | The nominal annual rate is divided across 52 periods |
| Daily | 365 per year | Uses a fixed 365-period modeled year |
| Continuous | Continuous | Uses exponential growth rather than discrete compounding periods |
Contribution frequency and compounding frequency can differ
The calculator does not require contributions and interest to use the same frequency. You can, for example, contribute every two weeks while a nominal rate compounds monthly.
Each contribution is placed on its own modeled time boundary. Growth between boundaries is calculated from the selected rate convention and compounding method.
This makes mixed-frequency scenarios possible without pretending that an abstract projection has actual deposit dates. If exact calendar dates, trading days, or institution-specific crediting rules matter, a date-based model is more appropriate.
Beginning versus end-of-period contributions
Contribution timing determines whether new money participates in the next period of growth immediately.
With beginning-of-period timing, the contribution enters before that contribution period's growth. End-of-period timing adds it after the period has elapsed.
The difference becomes larger as the contribution amount, rate, and length of time increase.
| Timing | Period order | Effect |
|---|---|---|
| End of period | Growth, then contribution | The new contribution begins growing during the next contribution period |
| Beginning of period | Contribution, then growth | Each contribution receives one additional contribution period of growth |
How to read the result
Projected ending balance is the final modeled value. Total contributions include the starting amount and every recurring contribution. Compound growth is the difference between those two figures.
Effective annual rate describes the annual effect of the rate mechanics. It does not include the effect of adding new money.
For nominal-rate calculations, the compounding comparison holds every other input constant and changes only the compounding frequency. That isolates how much the frequency itself changes the projection.
The growth schedule shows starting balance, contributions, modeled growth, and ending balance for each year, plus a final partial-year row when the selected term does not end on a full year.
Negative rates are useful for scenario analysis
Compound growth is not always positive. A negative annual rate can model a steadily declining balance and makes it possible to test the mathematical effect of a persistent loss assumption.
For example, $10,000 declining at an effective rate of 5% per year falls to $8,573.75 after three years if no new money is added.
A constant negative rate is still only a mathematical scenario. Real investment losses rarely arrive as the same percentage every year, and the sequence of gains and losses can materially affect an actual portfolio.
Compound interest calculator versus savings calculator
Use this calculator when the compounding mechanics themselves matter: nominal versus effective rates, continuous compounding, contribution frequency, contribution timing, negative-rate scenarios, or comparisons between compounding frequencies.
The Savings Calculator is designed around a different question. It starts from savings-account APY and can work backward from a savings goal to determine the monthly amount required.
Keeping those jobs separate makes each calculator easier to use and avoids treating an advertised savings APY as though it were a nominal investment rate.
What this projection does not model
One annual rate is applied for the complete projection. That is useful for comparing mathematical scenarios but is not a forecast of a market investment.
Actual investments can have changing and negative returns, fees, taxes, dividends, cash flows, and a sequence of returns that cannot be represented by one smooth annual percentage.
The calculator also does not adjust future balances for inflation. Use the result as a compound-growth model, then choose a more specialized investment or inflation tool when those additional assumptions matter.
Compound interest formulas
The calculator applies the appropriate growth factor over elapsed time, inserts recurring contributions at their modeled boundaries, and repeats the process through the selected term.
- Starting principal
- Projected future value
- Nominal annual rate as a decimal
- Periodic interest rate
- Discrete compounding periods per year
- Elapsed time in years
- Effective annual rate as a decimal
- Euler's number used for continuous compounding
- Balance after contribution period k
- Recurring contribution
- Growth factor across one contribution interval
- Starting principal plus recurring contributions
- Modeled growth above total contributions
Examples
Monthly contributions for 20 years
Initial investment: $10,000; contribution: $500 monthly at the end of each month; nominal annual rate: 7%; monthly compounding; time: 20 years.
The projected ending balance is about $300,850.72. Total contributions are $130,000 and compound growth is about $170,850.72.
The 7% nominal rate compounded monthly produces an effective annual rate of about 7.2290%.
Beginning versus end-of-month contributions
Initial investment: $0; contribution: $100 monthly; nominal annual rate: 12%; monthly compounding; time: 1 year.
Beginning-of-period contributions grow to about $1,280.93. End-of-period contributions grow to about $1,268.25.
Both scenarios contribute the same $1,200. The difference comes from how long each contribution remains exposed to growth.
Continuous compounding
Initial investment: $1,000; no recurring contributions; nominal annual rate: 12%; continuous compounding; time: 1 year.
The projected balance is about $1,127.50 and the effective annual rate is about 12.7497%.
A partial-year projection
Initial investment: $10,000; contribution: $250 monthly at period end; nominal annual rate: 4%; monthly compounding; time: 1 year 6 months.
After 18 months, the projected balance is about $15,247.10. Total contributions are $14,500 and modeled compound growth is about $747.10.
A negative-rate scenario
Initial investment: $10,000; no recurring contributions; effective annual rate: -5%; time: 3 years.
The projected balance falls to $8,573.75, a modeled decline of $1,426.25 from the initial amount.
Frequently Asked Questions
What is compound interest?
Compound interest is growth calculated on the original principal and on interest or growth already added to the balance.
What is the difference between nominal and effective annual rate?
A nominal annual rate does not include the complete effect of within-year compounding. An effective annual rate represents the actual percentage change over one year after compounding.
What is effective annual rate, or EAR?
EAR is the one-year return produced after applying the selected nominal rate and compounding frequency for a full year.
Why is compounding hidden when I choose effective annual rate?
An effective annual rate already contains the annual effect of compounding, so applying another compounding frequency would count that effect twice.
What is continuous compounding?
Continuous compounding is the mathematical limit of increasingly frequent compounding. It uses exponential growth rather than a fixed number of interest-crediting periods.
Can contributions and compounding use different frequencies?
Yes. For example, you can contribute every two weeks while using monthly, daily, or continuous compounding.
Can I contribute at the beginning of each period?
Yes. Open Additional and choose Beginning of period. Those contributions receive one additional contribution interval of modeled growth compared with end-of-period contributions.
Can I enter months as well as years?
Yes. The calculator supports terms from 1 month through 100 years, including periods such as 18 months or 12 years 6 months.
Can the interest rate be negative?
Yes. Rates down to -99.99% are supported for mathematical scenario analysis. Recurring contributions themselves must remain non-negative.
Does more frequent compounding always produce more growth?
For the same positive nominal annual rate, more frequent compounding produces a higher effective annual rate. With negative nominal rates, the relationship can behave differently.
Why can another compound interest calculator give a different answer?
Calculators may use different rate conventions, contribution timing, contribution frequencies, calendar assumptions, compounding methods, or rounding rules.
Can I use this to model stocks or funds?
It can model a constant-return scenario, but actual market investments have changing returns and may lose value. A smooth compound rate is not a market forecast.
Does the result include taxes, fees, or inflation?
No. The calculator isolates compound-growth mechanics and does not deduct taxes or fees or adjust the result for inflation.
What does the compounding comparison show?
It keeps the principal, contributions, timing, nominal annual rate, and term unchanged while recalculating the result with each supported compounding frequency.
What is included in the CSV?
The CSV includes each schedule period, months elapsed, currency, starting balance, contributions during the period, modeled growth, and ending balance.