How compound interest is calculated — step by step
Compound interest means each period’s interest is added to your balance, and the next period’s interest is calculated on that new, larger balance. The standard formula for a lump sum is:
FV = P × (1 + r/n)n×t
- P — the principal, your starting amount.
- r — the annual interest rate as a decimal (5% → 0.05).
- n — how many times per year interest compounds (daily = 365, monthly = 12, quarterly = 4, annually = 1).
- t — the number of years.
- Divide the rate by n, add 1, raise it to the power of n×t, and multiply by P to get the future value (FV).
If you also make regular deposits, each deposit compounds from the moment it is added. This calculator models deposits at the end of each period (an “ordinary annuity”, the usual textbook assumption) using:
FVdeposits = PMT × ((1 + i)N − 1) / i
where PMT is the deposit amount, N is the total number of deposits, and i is the effective growth rate per deposit period, derived from the same nominal rate: i = (1 + r/n)n/m − 1 with m deposits per year. The two results are added together. Our implementation is verified against a period-by-period simulation to the cent.
Worked example: $10,000 at 5% for 10 years
With annual compounding (n = 1), the balance grows like this:
| Year | Interest earned (5%) | Balance at year end |
|---|---|---|
| 1 | $500.00 | $10,500.00 |
| 2 | $525.00 | $11,025.00 |
| 3 | $551.25 | $11,576.25 |
| … | … | … |
| 10 | — | $16,288.95 |
Notice the interest itself grows every year — $500.00, then $525.00, then $551.25 — because each year’s 5% is applied to a bigger balance. That widening gap is the whole point of compounding. For comparison, simple interest (5% of the original $10,000 every year) would end at just $15,000.00.
Add contributions and the effect stacks: depositing $100 at the end of every month at 6% compounded monthly grows to $16,387.93 after 10 years, of which only $12,000 is your own deposits.
What people use this calculator for
- Savings goals — see how long an emergency fund or house deposit takes to reach a target, and how much a monthly top-up accelerates it.
- Retirement projections — model decades of monthly contributions at different assumed return rates, then flip on the inflation toggle to see the result in today’s money. Try our dedicated calculator with monthly contributions.
- Comparing accounts — a quoted 5% can mean different things; compare daily compounding against monthly compounding to see how frequency changes the effective yield (APY).
- Understanding debt — compounding also works against you: the same math shows how an unpaid balance grows when interest is charged on interest.
- Teaching the concept — the yearly table makes it easy to show students exactly where each dollar of growth comes from, and the share link lets you send a preset scenario.
Tips for realistic projections
A projection is only as good as its assumptions. Interest rates on savings products change over time, and investment returns swing widely from year to year even when the long-run average looks smooth. A useful habit is to run three scenarios — cautious, middle, optimistic — and plan around the cautious one. Remember that this tool assumes a constant rate, reinvested interest, no taxes, no fees and no withdrawals; real accounts differ on all five. And over long horizons, always check the inflation-adjusted figure: doubling your money in 25 years sounds great until you see what 25 years of inflation does to its purchasing power.
Frequently asked questions
What is compound interest?
Compound interest is interest earned on both your original money and on the interest that money has already earned. Each period, interest is added to the balance, and the next period’s interest is calculated on that larger balance — so growth accelerates over time instead of staying flat.
How do I calculate compound interest?
Use the formula FV = P × (1 + r/n)^(n×t), where P is the starting amount, r is the annual interest rate as a decimal, n is the number of compounding periods per year, and t is the number of years. For example, $10,000 at 5% compounded annually for 10 years is 10,000 × 1.05^10 = $16,288.95. Regular deposits are added with the ordinary-annuity formula: FV = PMT × ((1 + i)^N − 1) / i, where i is the growth rate per deposit period and N is the total number of deposits.
What is the difference between compound and simple interest?
Simple interest is paid only on the original principal, so $10,000 at 5% simple interest earns a flat $500 every year — $15,000 after 10 years. Compound interest is paid on principal plus accumulated interest, so the same $10,000 grows to $16,288.95 with annual compounding — $1,288.95 more, and the gap keeps widening the longer you stay invested.
Which compounding frequency should I choose?
Match whatever your account actually does: many savings accounts compound daily or monthly, bonds often compound semi-annually or annually. More frequent compounding at the same nominal rate always gives a slightly higher result, but the difference is small — $10,000 at 5% for 10 years gives $16,288.95 compounded annually versus $16,486.65 compounded daily, a gap of under $200. If you are unsure, monthly is a reasonable middle-ground assumption.
What interest rate should I enter?
For a savings account, CD, or bond, use the rate the institution quotes (ideally the APY with compounding set to annual, or the nominal rate with the matching frequency). For investment portfolios there is no guaranteed number: long-run averages for broad stock indexes are often cited in the 7–10% per year range before inflation, but past averages are not a promise of future returns — try a low and a high scenario instead of a single guess.
What does the "adjust for inflation" toggle do?
It divides the future value by (1 + inflation rate)^years to show what that money would buy in today’s prices. A projected $100,000 in 20 years at 2.5% yearly inflation has the purchasing power of about $61,000 today. The default 2.5% is editable — actual future inflation is unknown.
Is my financial data stored anywhere?
No. Every calculation runs in your browser — nothing you type is sent to or stored on any server. The optional "Copy shareable link" button simply encodes your inputs into the URL so you can reopen or share a scenario.
Everything on this site is an educational estimate, not financial advice. Returns are not guaranteed — verify important decisions with a qualified professional. Read more on the about page.