Core formula
A = P (1 + r/n)n·t
- Afuture value — what the investment grows to
- Pprincipal — the starting amount
- rannual interest rate, as a decimal
- nhow many times a year interest compounds
- ttime, in years
Compound interest,
watch your capital grow
Interest earning interest. Set your starting capital, rate, and schedule — the projection, chart, and breakdown update as you type.
Future investment value
—
Total interest earned
—
Initial balance
—
Total deposits
—
Total withdrawals
—
Effective annual rate
—
Time to double
—
All-time rate of return
—
Growth over time
Principal & deposits
Interest
Breakdown
| Year | Deposits | Withdrawals | Interest | Accrued interest | Balance |
|---|
Projections assume a constant rate and are for education only — markets do not pay a fixed percentage. Past performance never guarantees future results.
The formula,
behind the numbers
Every projection above comes from one identity. Here is how it works, piece by piece.
Worked example
Put $5,000 at 5%, compounded monthly, for five years:
5000 (1 + 0.05/12)60 = 6416.79
Interest earned is $1,416.79. Simple interest would have paid $1,250 — the extra $166.79 exists only because earlier interest itself earned interest. That gap widens every year you stay invested.
With regular deposits
FV = P(1+i)k + PMT · ((1+i)k − 1) / i
A recurring deposit adds an annuity term: each payment compounds for however many periods it has left. Here i is the rate per period and k the number of periods; a deposit made at the beginning of each period multiplies the term by one extra (1+i).
APY and the Rule of 72
APY = (1 + r/n)n − 1
Quoted rates are nominal. Compounding more often than yearly makes real growth higher: 5% compounded monthly truly pays 5.12% a year.
For a quick doubling estimate, divide 72 by the rate — at 5% that suggests about 14.4 years. The calculator computes it exactly: 13 years and 11 months.