Compound Interest Calculator
Calculate the future value of an investment, with optional periodic contributions.
| Period | Deposit | Interest | Balance | Cumulative Interest |
|---|
Formulas:
- Future Value (no contributions):
FV = PV × (1 + r)n - Future Value of annuity (contributions at end of each period):
FVannuity = PMT × ((1 + r)n − 1) / r - Total Future Value:
FVtotal = PV × (1 + r)n + PMT × ((1 + r)n − 1) / r(whenr > 0) - Accumulated Value:
Σk=0..n PV × (1 + r)k
How compound interest works
The intuition
When you earn interest, that interest is added to your balance. From the next period on, you earn interest on the original amount and on the interest you already earned. That is "compounding" — and it makes your money grow faster than simple interest, especially over long horizons.
For example, $1,000 at 5% for 10 years grows to $1,628.89 with annual compounding. At 0% (no compounding), it would stay at $1,000. The extra $628.89 is the compounding effect.
Why the rate is per period
If your period is one year, the rate is the annual rate. If your period is one month, the rate should be the monthly rate (annual rate ÷ 12). This calculator applies the rate exactly once per period, so it works for any compounding frequency — annual, quarterly, monthly, daily — as long as you stay consistent between rate and period.
End-of-period vs. start-of-period contributions
This calculator assumes end-of-period contributions: the deposit is added at the end of each period, so it does not earn interest in the period it is made. If you instead deposit at the start of each period, the result is slightly higher (by a factor of (1 + r)). Most retirement and savings calculators use the end-of-period convention.
Worked examples
Example 1: $1,000 at 5% for 10 years
Enter initialValue = 1000, periods = 10, growthRate = 5, contribution = (blank). Result: $1,628.89, with $628.89 of interest earned.
Example 2: $0 starting, saving $200/month for 30 years at 7% annual
With monthly compounding, set initialValue = 0, periods = 360 (30 × 12), growthRate = 0.5833 (7% ÷ 12), contribution = 200. Result: ~$244,000, of which $72,000 is your contributions and ~$172,000 is interest.
Example 3: How doubling time relates to the rate
At 7% annual, money doubles about every 10 years (the "Rule of 72": 72 ÷ 7 ≈ 10.3). At 10% annual, doubling takes about 7.2 years. This calculator's growth chart makes the curve obvious.
Related tools
The Compound Interest Calculator answers one specific question: how much will a sum grow over time at a given rate? Three situations where this is the right starting point:
- Retirement planning. Estimate the future value of regular savings over 20-40 years. Pair the result with the Present Value Calculator to convert a future nest-egg number back into today's dollars.
- Investment growth. Compare two return assumptions side by side: re-run the calculator with different rates to see how an extra 1% per year compounds over decades.
- Savings goal tracking. Plug in your target amount, work backwards: at what rate does a $10,000 deposit become $50,000 in 15 years?
For loans, mortgages, or any case where money flows out of a balance rather than in, use the Loan Calculator instead — the math is the same, but the result is framed as monthly payment and total interest rather than growth.
For a project with multiple positive and negative cash flows (an investment with upfront cost and downstream returns), use the NPV / IRR Calculator instead.
For a quick mental-math shortcut to estimate how long an investment takes to double, see The Rule of 72 Explained.
Frequently asked questions
How do I enter the interest rate?
Either way works: type 5 for 5% or 0.05 for 5%. The calculator detects which form you used.
What does "periodic contribution" mean?
It is an amount you add at the end of every period — for example, $100 saved every month into an investment account. Leave it blank for a one-time principal.
What's the difference between Future Value and Accumulated Value?
Future Value is the balance at the end of period n. Accumulated Value is the sum of the balance at the end of every period from 0 to n — useful when you want to know the total of all intermediate balances.
Does this include taxes or inflation?
No. The result is a pre-tax, nominal value. To estimate a real (inflation-adjusted) value, use a rate that is the nominal rate minus the inflation rate.