Compound Interest Calculator
Calculate how a principal grows with compound interest, with an optional recurring contribution and a simple-interest comparison.
How to Use
- Enter your starting principal, the annual interest rate, and how many years you're calculating for.
- Choose how often interest compounds — more frequent compounding (e.g. daily vs. annually) grows the balance slightly faster for the same nominal rate.
- Optionally add a recurring contribution — this is added once at the end of every compounding period you selected above (e.g. once a month if you chose monthly compounding). When you do, the time period must be a whole number of those periods (e.g. whole years for annual compounding, whole months for monthly), so every contribution has a clear period to land in.
- The result shows your final balance, total contributions, total interest earned, and a comparison against simple interest so you can see exactly what compounding adds.
Formula
- Periodic rate
- periodic_rate = annual_rate ÷ 100 ÷ periods_per_year
- Number of periods
- n = periods_per_year × years
- Final balance
- balance = principal × (1 + periodic_rate)^n + contribution × (((1 + periodic_rate)^n − 1) ÷ periodic_rate)
- Simple interest (for comparison)
- simple_interest = principal × annual_rate ÷ 100 × years
Worked Example
$10,000 principal, 5% annual rate, compounded annually, over 10 years, no recurring contributions.
- Periodic rate: 5 ÷ 100 ÷ 1 = 0.05
- Number of periods: 1 × 10 = 10
- Final balance: $10,000 × (1.05)^10 = $16,288.95
- Total interest earned: $16,288.95 − $10,000 = $6,288.95
- Simple interest for comparison: $10,000 × 0.05 × 10 = $5,000.00
Result: Final balance: $16,288.95 / Total contributions: $10,000.00 / Total interest earned: $6,288.95 / Simple interest comparison: $5,000.00
About This Tool
What this tool does
This calculator projects how a principal grows under compound interest — where interest is calculated not just on the principal, but also on interest already earned — over a chosen time period and compounding frequency, with an optional recurring contribution added each period.
When to use it
Use it to project how savings or an investment could grow over time, to compare how compounding frequency affects growth, or to see concretely how much more compound interest earns than simple interest on the same numbers.
What the result means
Final balance is what you'd have at the end of the period. Total contributions is your principal plus every recurring contribution you made along the way — the money you actually put in. Total interest earned is the difference: growth that came from the rate itself, not your own deposits. The simple-interest comparison line shows what the same principal alone (no compounding, no contributions) would earn under simple interest, so you can see compounding's effect directly — that line only claims compounding "earns more" when it verifiably does (it doesn't, for example, at a 0% rate or with only a single compounding period).
Assumptions & limitations
This assumes a fixed rate and fixed contribution amount for the entire period — real accounts often have rates that change over time. A recurring contribution is added once per compounding period you select (e.g. once a month for monthly compounding), always at the end of the period, not continuously throughout it. Because of that, whenever you enter a contribution above $0, the time period you enter must divide evenly into whole compounding periods (for example, whole years with annual compounding, or a whole number of months with monthly compounding) — a fractional period has no well-defined contribution, so it's rejected rather than silently rounded, dropped, or prorated. This restriction does not apply with no contribution, since balance growth alone over a fractional time period is ordinary continuous compounding. This tool is for projection and education only, not investment, tax, or financial advice, and it does not account for account fees, taxes on interest, or inflation.