Compound Interest Calculator
See how savings grow with compound interest, with or without regular deposits, and how much of the total is interest rather than your own money.
How to use this calculator
- 1Enter what you are starting with and the annual rate you expect.
- 2Choose how often interest compounds — savings accounts are usually monthly or daily, bonds often semi-annual.
- 3Add a regular deposit if you save every month; it is applied once per compounding period.
- 4Compare the "total you deposited" against "total interest earned" to see when compounding overtakes your own saving.
How the calculation works
A = P(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) − 1) / (r/n)]- A
- Final balance
- P
- Starting principal
- r
- Annual interest rate as a decimal (7% = 0.07)
- n
- Compounding periods per year
- t
- Time in years
- PMT
- Deposit made each compounding period
The first term grows the lump sum. The second is the future value of an ordinary annuity — the deposits.
For deposits at the start of each period (an annuity-due) the annuity term is multiplied by an extra (1 + r/n).
Continuous compounding replaces (1 + r/n)^(nt) with e^(rt); deposits are then modelled monthly.
Worked example
$10,000 for 20 years at 7%, compounded monthly
- 1.The monthly rate is 7% ÷ 12 = 0.583333…% and there are 20 × 12 = 240 periods.
- 2.A = 10,000 × (1 + 0.0058333)²⁴⁰ = 10,000 × 4.0387 = $40,387.39.
- 3.You put in $10,000 and earned $30,387.39 — the interest is three times the original deposit.
Result: $40,387.39, of which $30,387.39 is interest
What compound interest actually is
Simple interest is calculated only on the original amount you start with, for as long as you hold it. Compound interest is calculated on the original amount plus whatever interest has already been added — so once interest is paid into the balance, it starts earning interest of its own. That difference sounds small on paper but becomes the entire story over a long enough time horizon.
The gap between the two widens with time because compounding is not additive, it is multiplicative: each period’s growth builds on a slightly larger base than the period before. Over a few years the difference from simple interest is modest; over a few decades it can be the difference between doubling your money and multiplying it several times over.
The variables that shape the outcome
Four things determine how a balance grows under compound interest, and each one interacts with the others.
- Principal — the starting balance. Growth scales with it directly, but principal alone matters far less over long periods than the other three variables.
- Rate — the percentage the balance grows by in each period. Small differences in rate compound into large differences in outcome the longer the money is invested.
- Compounding frequency — how often interest is calculated and added to the balance — annually, monthly, daily, or continuously. More frequent compounding produces a slightly higher effective return, though the effect is smaller than most people expect.
- Time — the number of periods the money is left to grow. Of the four variables, time is consistently the most powerful, because its effect is exponential rather than linear.
Why starting early outweighs almost everything else
Because compounding is exponential, money given more time to grow does more work than money added later, even in larger amounts. A sum invested a decade earlier than a comparable, larger sum invested later can still end up ahead, simply because it had more compounding periods behind it. This is the practical reason financial guidance so consistently emphasises starting to save early over waiting for a "better" moment to start.
Where compound interest shows up in everyday finance
The same mechanism appears on both sides of a household balance sheet — working for you in some places and against you in others.
- Savings and money market accounts — interest is typically compounded daily or monthly and added to the balance, where it then earns interest itself.
- Bonds and certificates of deposit — often compound less frequently — semi-annually is common for many bonds — which is one reason comparing the effective annual rate, not just the quoted rate, matters when comparing products.
- Credit card debt — compounds the same way, but against you — unpaid interest is added to the balance and itself starts accruing interest, which is why revolving debt can grow quickly if only minimum payments are made.
What this assumes, and where it stops
Assumptions
- The rate stays constant for the whole period.
- Interest is reinvested rather than withdrawn.
- Deposits happen exactly once per compounding period and never miss.
- No tax, platform fees or inflation are deducted. Enter a real (after-inflation, after-fee) rate if you want the result in today’s money.
Limitations
- Real investment returns are volatile; a constant rate overstates certainty even when the average is right.
- Tax on interest or capital gains can materially reduce the outcome and varies by country and account type.
- Introductory and bonus savings rates that expire after a year are not modelled.
- The sequence of returns matters when you are also withdrawing — this tool does not model withdrawals.
Common questions
What is the difference between the interest rate and APY?
The interest rate is the nominal, quoted rate. APY (effective annual rate) is what you actually earn once compounding is taken into account. At 7% compounded monthly the APY is 7.229% — the extra comes from earning interest on interest within the year. APY is the fair number for comparing accounts with different compounding frequencies.
Does compounding more often make a big difference?
Less than people expect. Going from annual to monthly compounding at 7% adds about 0.23 percentage points a year. Going from monthly to daily adds about 0.01. The rate and the time period dominate; the frequency is a rounding detail by comparison.
How do I account for inflation?
Enter a real rate instead of a nominal one: subtract expected inflation from your expected return. A 7% return with 3% inflation is roughly a 4% real rate, and the result then shows the balance in today’s purchasing power.
Sources
- Compound interest and the rule of 72 — US Securities and Exchange Commission
Formula and content last reviewed on .
Results are estimates for information only, not professional advice.
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