Compound Interest Calculator

Compound interest: why time and frequency matter

Compound interest means you earn “interest on interest”. The more often compounding occurs within a year, the slightly higher the effective growth, all else equal. For long horizons—retirement savings, index-fund scenarios, or debt that capitalizes—small rate or frequency differences dominate outcomes.

Formula core: Future value with periodic compounding uses FV = PV(1 + r/m)^(m×t) for lump sums; monthly contributions add a series of growing deposits (this tool computes both numerically). The annual percentage yield (APY) rises versus the stated APR when compounding happens more than once per year.

Use cases: projecting 401(k)/IRA balance paths, stress-testing savings rate changes, teaching students about exponential growth, or sanity-checking marketing claims (“double your money in X years” — solve for rate or time).

Common pitfalls: confusing nominal APR with APY; ignoring fees; assuming constant returns (real markets fluctuate); forgetting tax drag on interest in taxable accounts. Use this calculator as a baseline, not a forecast guarantee.

Contrast with simple interest: simple interest ignores interest-on-interest: suitable for some short bonds or punitive late-fee math, but most savings and loans you meet day-to-day are compound in practice. When comparing loans, look at amortization schedules rather than headline rates alone.

Lump sum with compounding m times per year: FV = PV × (1 + r/m)^(m·t). With periodic payment A at end of each period (simplified monthly case shown in tool): use iterative accumulation or closed-form annuity FV formulas depending on timing.

What the calculator does

Your starting amount compounds at the chosen frequency — annually, semi-annually, quarterly, monthly or daily — using FV = P × (1 + r/n)^(n·t). A monthly addition is paid in at the end of every month and earns interest from then on; additions are always monthly, whichever compounding frequency you choose, and the frequency only changes how often interest is credited. The chart shows the balance at the end of each year, up to 40 years.

Worked examples

• $10,000 at 7%, compounded monthly, for 20 years grows to $40,387.39 — about four times the original.
• Add $200 a month and the balance reaches $144,572.72: you paid in $58,000 and $86,572.72 is interest.
• Starting earlier beats saving more: $300 a month at 7% for 30 years gives $365,991; the same $300 a month for 40 years gives $787,444 — more than double, for only $36,000 more in contributions.

How much compounding frequency matters

$10,000 at 5% for 10 years:

Annually    $16,288.95
Quarterly   $16,436.19
Monthly     $16,470.09
Daily       $16,486.65

Going from annual to daily compounding adds under $200 over ten years. The rate and the time invested matter far more than the frequency — which is why comparing accounts by APY, which already includes compounding, is the fair comparison.

The Rule of 72 estimates doubling time as 72 ÷ rate: at 7% that is 10.3 years, against an exact 10.24 years.

Keeping projections realistic

• Investment returns are not fixed. A constant 7% is a long-run assumption; real portfolios rise and fall, and the order of good and bad years matters when you are adding or withdrawing money.
• Fees compound too. A 1% annual fee on a 7% return leaves 6%, which over 30 years ends roughly a quarter lower.
• Inflation: subtract expected inflation from the rate to see the result in today’s money.
• This is an educational estimate, not financial advice.