Compound interest calculator
Estimate investment growth with compounding and regular contributions.
Fill in the fields and the result will appear here automatically.
Capital growth needs a distinction between your contributions and earned interest. Contribution frequency and capitalization frequency are separate here: money deposited midway through a year does not earn a full year of interest. The table shows yearly checkpoints and the actual final period. Use it to compare illustrative constant rates and contribution plans; it does not predict market returns.
How it works
Formula and logic
The monthly rate is r = annual rate / 100 / 12. Each month, principal balance B earns B × r in accrued interest. Accrued interest joins capital every 1, 3 or 12 months according to capitalization frequency. Contributions are added at the end of their interval, after interest accrual, and earn nothing before they are deposited. Without contributions, complete periods follow F = P × (1 + j / k)^N: P is initial capital, j the annual rate as a fraction, k capitalizations per year and N complete periods. When contribution and capitalization intervals match, contributions have future value C × ((1 + i)^N − 1) / i, where C is the contribution at period end and i the period rate. Mixed frequencies use monthly cash flows. Interest for an unfinished final capitalization period is included at the end without early capitalization. Profit is final capital minus all contributions. Inflation, taxes, fees and negative-return years are not modeled.
Example
Illustrative currency units: initial capital 1,000, nominal annual rate 12%, term 1 year, monthly contribution 100 and annual capitalization. Initial capital earns 120. Contributions earn for 11, 10, …, 0 months: 100 × 0.01 × (11 + 10 + … + 0) = 66. Invested funds are 2,200, profit 186 and final capital 2,386. With contributions of 100 each quarter instead, invested funds are 1,400, profit 138 and final capital 1,538. Partial-period boundary: without contributions, 1,000 at 12% with annual capitalization over 1.5 years becomes 1,120 after year 1, plus 67.20 accrued in the next half-year; final capital is 1,187.20, displayed as 1,187.
Fields and units
- Initial amount — $
- Rate — %
- Compounding frequency — list option
- Years — years
- Regular contribution — $
- Frequency — list option
How to use
- — Enter initial capital and a constant nominal annual rate. This model accepts nonnegative rates.
- — Choose a term up to 1,000 years. A fractional year must equal a whole number of months.
- — Set capitalization frequency separately from contribution amount and frequency: monthly, quarterly or annually.
- — Contributions are made at the end of their interval. Compare invested funds with profit; longer tables keep the actual final period after the first 30 years.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- SEC Investor.gov (US): educational inputs for capital, contributions and compounding
- Limitation
- Illustrative constant nonnegative nominal-rate model with contributions at period end. The result is neither a market forecast nor guaranteed income; losses, inflation, taxes and fees are excluded.
FAQ
Why does a monthly contribution not earn a full year under annual capitalization?
Interest accrues only after money is in the balance. A contribution at the end of month 1 earns for the next 11 months. Capitalization sets when earned interest joins principal; it does not move a contribution’s deposit date backward.
How should I choose a rate for a capital-growth scenario?
Use your own illustrative rates and keep the contribution plan equal when comparing them. The calculator does not determine a realistic market return: it holds a nonnegative rate constant and excludes losses or fluctuations.
Why is final capital different from the invested amount?
Invested funds are initial capital plus contributions actually made. The difference from the final amount is modeled interest. Both are nominal amounts before taxes and costs, not purchasing power after inflation.