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Compound Interest Calculator
Estimate future value from a fixed annual rate, compounding frequency and optional per-period contributions, with a simple-interest comparison and period schedule.
Growth assumptions
Future value
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Compound growth is A = P(1 + r/n)^(nt), where r is the annual rate as a decimal, n is compounds per year and t is years. Contributions at the beginning of each period earn one extra period of interest versus end-of-period contributions. This assumes a fixed rate; real trading returns are not fixed and can be losses.
How it works
What compound interest measures
Compounding means each period's interest is added to the balance, so future interest is earned on both the original principal and prior interest. The calculator is a fixed-rate math model. It should not be read as a promise that trading or investing can produce a steady rate.
The formula without contributions
A = P(1 + r/n)^(nt)
P is the starting principal, r is the annual rate divided by 100, n is compounds per year and t is years. Continuous compounding uses A = P × e^(rt).
The formula with per-period contributions
For end-of-period contributions, also called an ordinary annuity:
A = P(1+i)^N + PMT × ((1+i)^N - 1) / i, where i = r/n and N = nt.
For beginning-of-period contributions, the annuity part is multiplied by (1+i). If i = 0, the contribution term degrades cleanly to PMT × N so there is no division by zero.
Schedule check
The schedule is built period by period: add the contribution first for beginning timing, calculate interest, then add the contribution after interest for end timing. The last schedule balance should match the closed-form result within floating-point tolerance.
Worked example - no contributions
Starting with 10,000 at 8% compounded monthly for 10 years gives 10,000 × (1 + 0.08/12)^120 = 22,196.40.
Worked example - monthly contributions
Starting with 1,000 at 6% compounded monthly for 1 year, with 100 added at the end of each month, gives a final value of about 2,295.23. Beginning-of-period contributions would be higher because each contribution earns one extra month of interest.
Common mistakes
- Using 8 instead of 0.08. The input is a percentage for humans, but the formula uses
annualRatePct / 100. - Mixing beginning and end timing. Beginning contributions earn interest in the same period; end contributions do not.
- Forgetting the zero-rate branch. When the period rate is zero, the annuity denominator would be zero, so the contribution term becomes
PMT × N. - Reading a fixed rate as a trading forecast. Real trading returns are variable, costs matter, and losses can interrupt or reverse compounding.
Frequently asked questions
What is the compound interest formula?
A = P(1 + r/n)^(nt). With end-of-period contributions, add PMT × ((1+i)^N - 1) / i, where i = r/n.What is the difference between beginning and end contributions?
What happens when the rate is zero?
PMT × N. Final value is principal plus all contributions.Does this mean trading can compound steadily?
Why include simple interest?
P × (1 + r × years) with no interest-on-interest effect, making the compounding difference easier to see.