Compound Interest Calculator
Calculate how your savings or investment grows with compound interest, including optional recurring contributions, annual or monthly compounding, and total interest earned.
How It's Calculated
Formula
FV = P \left(1 + \dfrac{r}{n}\right)^{nt} + PMT \left[\dfrac{\left(1 + \dfrac{r}{n}\right)^{nt} - 1}{\dfrac{r}{n}}\right]Compound interest is interest calculated on both your original balance and on interest you've already earned, so growth accelerates over time instead of staying flat. This calculator projects how an initial principal grows under compound interest, optionally adding a fixed deposit at the end of every compounding period. Each deposit is applied at the end of its period (an "ordinary annuity") — a deposit made at the end of month one doesn't start earning interest until month two. Choose annual or monthly compounding, enter the nominal annual rate and duration, and the calculator returns your final balance, how much of that is money you put in, and how much is interest earned on top of it.
Worked Examples
Lump sum only: $10,000 principal, 5% annual rate, monthly compounding, 10 years
- Periodic rate r/n = 0.05 / 12
- Total periods n·t = 12 × 10 = 120
- FV = 10000 × (1 + 0.05/12)^120 ≈ $16,470.09
- Total principal contributed = $10,000 (no recurring deposits); total interest earned ≈ $6,470.09
Recurring deposits, no starting balance: $0 principal, $100/month, 6% annual rate, monthly compounding, 5 years
- Periodic rate r/n = 0.06 / 12 = 0.005
- Total periods n·t = 12 × 5 = 60
- FV = 100 × [((1.005)^60 − 1) / 0.005] ≈ $6,977.00
- Total principal contributed = 60 × $100 = $6,000; total interest earned ≈ $977.00
Frequently Asked Questions
When do my deposits start earning interest?
Each periodic deposit is credited at the end of its compounding period, not the beginning. That means a deposit made during the current period doesn't earn interest until the next period begins. This convention (an "ordinary annuity") is the standard default used in most savings and investment calculators.
What's the difference between annual and monthly compounding?
Annual compounding calculates and adds interest once a year; monthly compounding does it 12 times a year. For the same nominal annual rate, monthly compounding produces a slightly higher final balance, because interest starts earning its own interest sooner and more often.
Should I enter my bank's APY or the nominal rate?
Enter the nominal annual rate — the stated rate before any compounding effect is factored in (e.g. "5" for 5%). This calculator derives the actual per-period rate itself based on your chosen compounding schedule, so entering an already-compounded APY would double-count the compounding effect.
Can I model a one-time investment with no ongoing deposits?
Yes — set the periodic deposit to 0. The calculator then computes pure compound growth on your initial principal alone, with no annuity contribution term.
Why is "total interest earned" not just balance minus what I typed in?
It is exactly that: total interest earned equals the final accumulated balance minus total principal contributed, where total principal contributed is your initial principal plus every periodic deposit you made. It isolates the growth that compounding itself produced, separate from money you actually deposited.