Compound Interest Calculator - Future Value with Contributions

How to use this tool

1. Enter starting principal. Enter the amount you are starting with. You can enter 0 if you are starting from scratch with regular contributions only.
2. Set the interest rate. Enter a nominal annual interest rate or return. The calculator shows the effective annual yield implied by your selected compounding frequency. These rates are assumptions, not forecasts.
3. Choose compounding frequency. Select the compounding frequency for the nominal annual rate. Monthly deposits grow at the corresponding equivalent monthly rate; actual account credit dates may differ.
4. Add a monthly contribution. Enter an optional monthly deposit. Deposits earn interest as the balance grows, but this fixed-return model does not simulate dollar-cost averaging across changing prices; use a dollar-cost averaging calculator for that.
5. Review the year-by-year table. Scroll down to see exactly how your balance grows each year, broken down into contributions and interest.

How to use the compound interest calculator

Enter your starting principal, expected annual interest rate, and investment period. Choose how often interest is compounded. Optionally add a monthly contribution. The future value, total interest earned, and a year-by-year breakdown update as you type.

The compound interest formula

For a lump sum with discrete compounding, the standard formula is:

FV = P × (1 + r/n)^(nt)

Here FV is the future value, P is the starting principal, r is the nominal annual rate as a decimal, n is the selected compounding frequency per year, and t is the number of years. The corresponding effective annual yield is (1 + r/n)^n − 1; for continuous compounding it is e^r − 1.

This calculator advances the balance in 12 monthly steps per year. Each month it multiplies the balance by g = (1 + r/n)^(n/12), or g = e^(r/12) for continuous compounding. A beginning-of-month deposit is added before that month’s growth; an end-of-month deposit is added after it. With no deposits, this produces the familiar lump-sum formula. The “Annually” option still applies the equivalent annual yield monthly, so deposits made during the year earn growth before year-end. This interpolates growth between compounding dates; it does not model the exact dates when an account credits interest. The displayed doubling time uses the same interpolation and excludes deposits.

For monthly compounding and end-of-month deposits, the familiar contribution formula also applies: PMT × ((1+r/12)^(12t) − 1) / (r/12), where PMT is the monthly deposit. The calculator uses the month-by-month loop for every frequency, including when the rate is 0%, so it does not divide by the rate.

The power of compounding: example

These projections use the same inputs as the calculator’s annual default, with monthly deposits set to $0 and only the compounding frequency changed.

Why regular contributions matter

Adding a monthly contribution can substantially increase the ending balance. With $10,000 at 7% for 30 years, the calculator’s default annual frequency and a $500 deposit at each month-end project about $660,849; choosing monthly compounding projects about $691,150. The annual case is about 8.7 times the $76,123 lump-sum result. Starting each monthly deposit at the beginning of the month raises those totals by about 0.5%, since each deposit gets one extra month to grow. This is regular saving under a constant assumed return, not dollar-cost averaging across changing share prices. For that, see the dollar-cost averaging calculator.

Compounding frequency comparison

More frequent compounding raises the effective annual yield, but the difference narrows at higher frequencies. For the $10,000 example above, monthly compounding ends about 6.6% higher than annual compounding. Moving from daily to continuous changes the 30-year result by about $16, or 0.02%. Savings accounts may compound daily or monthly; investment return assumptions are often quoted as annual rates, so compare like with like.

Inflation-adjusted (real) returns

A nominal return is not the same as an increase in purchasing power. Enter an expected annual inflation rate to see the future value expressed in today’s dollars. The real annual rate uses the Fisher equation with the effective annual yield implied by the selected frequency:

Real rate = (1 + effective annual yield) / (1 + inflation) − 1

For example, at 7% with annual compounding and 3% inflation, the real annual rate is about 3.88%. A $10,000 balance that reaches $76,123 after 30 years has purchasing power of about $31,361 in today’s dollars. Subtracting inflation from the nominal rate gives a rough 4% shortcut; applying that shortcut instead would produce about $32,434. Inflation is an assumption, not a forecast, and the tool leaves the headline projection in nominal dollars. For historical purchasing-power comparisons, use the inflation calculator.

Tax drag on compounding

Taxes reduce compounding in taxable accounts because a portion of gains is paid to the government each year, reducing the principal that compounds going forward.

• Tax-deferred accounts (401k, Traditional IRA): contributions and growth are not taxed until withdrawal. The full principal compounds year-over-year, significantly increasing the ending balance compared to a taxable account with the same gross return.
• Tax-free accounts (Roth IRA, Roth 401k): contributions are post-tax but growth and qualified withdrawals are never taxed again. Ideal for assets expected to appreciate significantly.
• Taxable brokerage accounts: dividends and short-term capital gains are taxed as ordinary income each year. Long-term capital gains are taxed at lower preferential rates, but taxes still reduce the compounding base annually.