Future Value Calculator: FV, PV, Payment, Rate, Periods

About the Future Value Calculator

The Future Value Calculator solves the time value of money equation. Enter a starting amount, a regular payment, an interest rate and a number of periods, and it shows what the balance grows to. It can also solve the equation the other way round: choose what you want to find and it works out the present value, the payment, the interest rate or the number of periods from the other values.

The regular payment can be a deposit into the account or a withdrawal from it, made at the end or the start of each period. Payments can be annual, semiannual, quarterly or monthly, and the interest can compound annually, semiannually, quarterly, monthly or daily, even when that differs from the payments. The answer is shown to the cent with no currency symbol, together with the nominal annual rate and the effective annual rate.

The calculator assumes the same interest rate for every period and ignores fees and taxes, so the results are estimates.

How to use it

The formulas

The annual rate $r$, compounded $c$ times a year, becomes a rate per payment period $i$ when there are $p$ payments a year:

$$i = \left(1 + \frac{r}{c}\right)^{c/p} - 1$$

With a starting amount $PV$, a payment $PMT$ (positive for deposits, negative for withdrawals) and $n$ periods, the future value is

$$FV = PV(1 + i)^n + PMT \cdot \frac{(1 + i)^n - 1}{i} \cdot (1 + i \cdot t)$$

where $t$ is 1 when payments are made at the start of each period and 0 at the end. The present value, payment and number of periods come from rearranging this equation. The rate has no closed form, so the calculator finds it by bisection between −99% and 100% per period.

Worked examples

• A lump sum. 10,000 at 5% a year for 10 years grows to $10{,}000 \times 1.05^{10} = 16{,}288.95$.
• Monthly deposits. 100 a month for 120 months at 6% compounded monthly grows to 16,387.93, or 16,469.87 when each deposit is made at the start of the month.
• Different compounding. 100 a month for a year at 12% compounded annually grows to 1,264.65; at 8% compounded quarterly it grows to 1,244.69.
• The deposit needed. To reach 100,000 in 10 years at 6% compounded monthly, save 610.21 a month.
• How long savings last. 100,000 earning 6% compounded monthly pays out 1,000 a month for 138.98 months.

Related calculators

To see the balance grow year by year with regular deposits, use the Compound Interest Calculator. For a loan repaid in equal monthly instalments with an amortization schedule, use the Loan Calculator. To work out what a future sum is worth today, the Present Value Calculator opens this tool with the present value selected.

Privacy

Nothing is uploaded; every calculation runs in your browser and never leaves your device. The numbers you type stay on this page and are gone when you close or reload it.

Frequently asked questions