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See how a lump sum plus optional monthly contributions grows over time with compounding.
A compound interest calculator shows how an investment or savings balance grows when the interest earned each period is added back to the principal — so the next period's interest is calculated on a larger base. It's the math behind why a retirement account contributed to steadily over thirty years ends up many times larger than the sum of the contributions: every dollar of interest starts earning interest of its own. This calculator accepts a starting amount, an annual rate, a term in years, an optional monthly contribution, and a compounding frequency (annually, quarterly, monthly, or daily). It returns the final balance, the total you contributed, the total interest earned, and the effective annual yield. Everything runs in your browser — nothing is sent to a server.
Type the lump sum you're starting with. If you're modelling pure contributions with no initial deposit, enter 0 and the calculator will still work — it'll grow only what you add.
Use the expected annual rate as a percent. A high-yield savings account runs ~4–5%, a diversified index fund historically ~7% real / ~10% nominal over long periods, and individual stocks swing much wider.
The longer the horizon, the more compounding dominates the contributions. Try 10, 20, and 30 years to see how dramatically time shifts the final balance.
This simulates paycheck deposits into a savings or brokerage account. It's added before each compounding step, so it starts earning interest immediately.
Monthly is typical for savings accounts; daily is common for cash-management accounts; quarterly or annually is how some bonds and CDs are quoted. Higher frequencies produce slightly higher results at the same nominal rate.
The final balance, total contributed, total interest, and effective APY update instantly. Open the year-by-year schedule to see how much growth is contribution vs. interest in each year.
without contributions:
A = P × (1 + r/n)^(n·t)
with end-of-period contributions:
A = P × (1 + r/n)^(n·t)
+ PMT × [((1 + r/n)^(n·t) − 1) / (r/n)]
where:
A = final balance
P = initial principal
r = annual interest rate (decimal)
n = compounding periods per year
t = number of years
PMT = per-period contribution
this calculator applies a monthly contribution converted
to match the compounding frequency you pick.Compounding means each period's interest becomes part of the base on which the next period's interest is computed. With a zero rate the growth is linear (just the contributions); with any positive rate the curve bends upward over time, more steeply the longer the horizon. The 'effective APY' reported below normalises across compounding frequencies so you can compare a daily-compounded 5% account to a monthly-compounded 5.05% account on equal footing.
Reference: Wikipedia — Compound interest
| Inputs | Final balance / interest |
|---|---|
$10,000 · 5% · 10 yrs · no contributions · monthly | $16,470 · $6,470 interest Lump sum only. Interest is 39% of the final balance. |
$5,000 · 7% · 30 yrs · $500/mo · monthly | $653,780 · $467,780 interest Long horizon plus steady contributions — interest eventually dwarfs the $185,000 total contributed. |
$0 · 8% · 40 yrs · $300/mo · monthly | $1,047,302 · $903,302 interest Classic 'millionaire by retirement' scenario from $300/month alone. |
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