Compound Interest & Future Value Calculator
Calculate the future value of an investment, with optional periodic contributions.
This page is scoped to recurring deposits: a starting balance that compounds while a contribution is added at the end of every period — the usual pattern for savings and investment plans. If your scenario is a single lump sum grown to a target date, the Future Value Calculator frames the same compound math around the lump sum and its formula. Both calculators can handle either input; pick the one that matches your primary scenario.
Compound interest is the engine behind long-term wealth growth: every period, interest is added to the balance, and from the next period on, that interest also earns interest. For starting principal PV, periodic rate r, n periods, and end-of-period contribution PMT: FV = PV × (1 + r)n + PMT × ((1 + r)n − 1) / r when r > 0. Example: 1,000 at 5% for 10 years grows to 1,628.89, of which 628.89 is interest. Saving 200 per month for 30 years (360 periods) at 7% annual — rate per period = 0.5833% — reaches about 244,000, with 72,000 of personal contributions and 172,000 of accumulated interest. The rate must match the period: annual rate for yearly periods, annual rate ÷ 12 for monthly periods. Contributions land at the end of each period, so the first deposit does not earn interest in its own period. At 2.5% inflation, the $1,628.89 above is about $1,272.49 in today's money — $356.40 erosion.
| 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.
The future value formula
The future value compound interest formula is FV = PV × (1 + r)n: a present value PV grows at rate r for n periods. With $1,000 at 5% per year for 10 years, the future value is $1,000 × 1.0510 = $1,628.89.
When you deposit an amount PMT at the end of every period, the future value formula becomes FV = PV × (1 + r)n + PMT × ((1 + r)n − 1) / r — the second term is the future value of an ordinary annuity. The full formula list this calculator uses appears in the Formulas section above the schedule.
Two conventions matter when applying the formula: r must match the period length (annual rate for yearly periods, annual ÷ 12 for monthly), and deposits are assumed to land at the end of each period. Both are explained in How compound interest works above.
Compound interest with inflation
The calculator reports a nominal future value — inflation is not deducted. To use this compound interest calculator with inflation in mind, estimate the real (inflation-adjusted) result in one of two ways:
- Deflate the result. Divide the nominal future value by
(1 + i)n, where i is the annual inflation rate. $1,628.89 after 10 years at 2% inflation is $1,628.89 ÷ 1.0210 ≈ $1,336 in today's purchasing power. - Use a real rate. Approximate the real rate as the nominal rate minus inflation (5% − 2% = 3%) and compound at that. The exact form is
(1 + rnominal) ÷ (1 + i) − 1; the subtraction rule is close enough at low rates.
For the reverse move — expressing a future amount in today's dollars with a discount rate of your choosing — see the Present Value Calculator.
To see every inflation number at once — the future cost of the same basket, the buying power of today's money, the cumulative inflation over the horizon and the real return your nominal rate leaves after inflation — use the inflation calculator. It is the direct answer to "compound interest calculator with inflation": run the nominal growth here, then deflate the result there.
Compound interest on TI-84 and Excel
You can calculate compound interest and future values directly on a TI-84 graphing calculator or in Excel using standard financial functions:
- TI-84 TVM Solver (Lump Sum):
- Press
APPS, select1:Finance…, and pressENTERfor1:TVM Solver…. - Enter
N = 10,I% = 5,PV = -1000,PMT = 0,P/Y = 1,C/Y = 1. - Move cursor to
FVand pressALPHAthenENTER(SOLVE) to calculate $1,628.89.
- Press
- Excel Formula (Lump Sum): Type
=FV(5%, 10, 0, -1000)into any cell to return $1,628.89. - TI-84 TVM Solver (Monthly Annuity): For saving $200/month over 30 years at 7% annual return, enter
N = 360,I% = 7,PV = 0,PMT = -200,P/Y = 12,C/Y = 12. Solving forFVyields ~$244,000 ($243,994.20). - Excel Formula (Monthly Annuity): Type
=FV(7%/12, 360, -200)to compute the same ~$244,000 future value.
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 Period Unit to Months, initialValue = 0, periods = 360 (30 × 12), growthRate = 0.5833333333% (7% ÷ 12), contribution = 200. Result: ~$244,000 ($243,994.20), of which $72,000 is your contributions and ~$172,000 is interest. At 2.5% annual inflation, that $243,994.20 is about $116,322.45 in today's money, with $127,671.75 of inflation erosion over the 30 years.
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
For a dedicated FV formula with explicit support for ordinary annuity contributions, see the future value calculator.
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 the rate apply per year, per month, or per period?
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).
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. The calculator's Inflation Rate field does this automatically — fill it in and the result area shows today's purchasing power and the inflation erosion.
What is the future value formula with compound interest?
FV = PV × (1 + r)n, where PV is the present value, r the per-period rate, and n the number of periods. With recurring end-of-period deposits PMT, add PMT × ((1 + r)n − 1) / r.
How do I account for inflation?
The result is nominal. For a real (inflation-adjusted) figure, divide it by (1 + i)n for inflation rate i — or enter an approximate real rate (nominal − inflation). Details in Compound interest with inflation. The calculator's Inflation Rate field does this automatically — fill it in and the result area shows today's purchasing power and the inflation erosion.
How do I add an inflation rate to the calculation?
Enter the annual inflation rate in the optional Inflation Rate field (e.g., 2.5 or 0.025). The result area then shows today's purchasing power (FV ÷ (1 + i)n, n = years — when Period Unit is Months, n = periods ÷ 12) and the inflation erosion, and the chart adds a real-value line. Leave the field blank to keep the nominal-only view.
How is this different from the Future Value Calculator?
Mathematically, neither: both compute FV = PV × (1 + r)n with an optional periodic-contribution term, so either tool can model a lump sum or recurring deposits. The difference is framing — this page organizes the period-by-period schedule, total contributions and interest earned around a savings plan, while the Future Value Calculator organizes the same math around a single lump sum and its formula. Use this page when recurring deposits drive your question, and the other when a one-time investment does.