Compound interest means each period's interest gets added to the balance before the next period's interest is calculated — so you eventually earn interest on interest already earned, not just on the money you originally put in. That reinvestment is what bends a straight-line savings plan into a curve.
The Formula, Applied Step by Step
This calculator uses A = P × (1 + r/n)nt + c × [((1 + r/n)nt − 1) / (r/n)], where P is your starting principal, r is the annual rate as a decimal, n is compounding periods per year, t is years, and c is your monthly contribution. The first term grows your initial lump sum; the second term grows the stream of monthly deposits, each compounding for however long it's been sitting in the account.
Simple vs. Compound, Side by Side
Put $5,000 in at 6%, compounded monthly, adding $150 a month, for 15 years:
| Method | Formula Used | Result After 15 Years |
|---|---|---|
| Simple interest | P + P·r·t + c·12·t | ≈ $36,500 |
| Compound interest (monthly) | P(1+r/n)nt + c[((1+r/n)nt−1)/(r/n)] | ≈ $55,900 |
Same principal, same contributions, same nominal rate — the roughly $19,400 gap is purely the effect of interest earning interest. For a side-by-side calculator that isolates simple interest on its own (no reinvestment, useful for things like short-term promissory notes), see the Simple Interest Calculator.
A Faster Sanity Check: The Rule of 72
If you just want a rough sense of how long a lump sum takes to double — without entering contributions or compounding frequency — divide 72 by your interest rate. At 6%, that's 12 years; this calculator's monthly-compounding math will actually get there slightly faster. The Rule of 72 Calculator is the quick mental-math version of what this page computes precisely.
Where the Model's Assumptions Can Mislead You
- It assumes a constant rate for the entire horizon — real investment returns fluctuate year to year even when the long-run average matches your input.
- It doesn't subtract taxes or fund fees; both quietly erode compounding if you don't account for them separately.
- Contributions are assumed to happen every month without interruption for the full term you enter.
Further reading: Investopedia — Compound Interest and Bankrate — Compound Savings Calculator.
Disclaimer: This calculator and the notes above are for educational purposes only and should not be considered financial advice. Actual investment returns vary and are never guaranteed. Consult a qualified financial advisor before making investment decisions.