Future Value Calculator
Calculate the future value of a lump-sum deposit or a series of equal payments (annuity) at a given rate. See the FV formula and step-by-step math.
What is future value?
Future value (FV) answers the question: "if I deposit money today (or a fixed amount every period), how much will it be worth after n periods at a given interest rate?" It's the forward-looking half of the time-value-of-money pair — the other half, present value, answers the reverse question by discounting a future amount back to today.
This calculator covers two common cases: a lump-sum deposit made once, and an annuity — equal payments made every period (like a monthly retirement contribution).
The formula: lump sum
- FV — future value (what the deposit grows into)
- PV — present value (the amount deposited today)
- r — interest rate per period, as a decimal (rate ÷ 100)
- n — number of periods
Example: deposit $10,000 today at 5% per period, for 10 periods: FV = 10,000 × (1.05)^10 ≈ $16,288.95. The interest earned is FV − PV = $16,288.95 − $10,000 = $6,288.95.
The formula: annuity (equal payments)
- PMT — the payment made every period
- r, n — same meaning as above
Each payment compounds for a different number of remaining periods (the first payment earns interest for n−1 periods, the last payment earns none), and this formula sums all of them at once — the same geometric-series shortcut behind the loan-payment calculator's amortization math, run forward instead of backward.
Example: deposit $100 every period at 0.5% per period, for 120 periods (10 years, monthly): FV = 100 × ((1.005)^120 − 1)/0.005 ≈ $16,387.93. You contributed $100 × 120 = $12,000 total, so interest earned is $16,387.93 − $12,000 = $4,387.93.
Common mistakes
- Confusing PV (lump-sum) with PMT (annuity). These are different modes with different formulas — a single deposit that compounds once isn't the same as recurring payments that each compound separately.
- Mismatching the rate and period units. A monthly rate must be paired with a count of months, not years — the compounding formula has no way to know your intent otherwise.
- Forgetting that a 0% rate is valid. It's not an error condition; it just means no interest is earned, so future value equals the total amount contributed.
- Mixing up future value with present value. Future value projects money forward (multiplies by the growth factor); present value discounts it backward (divides by the growth factor) — they're inverse operations, not the same calculation run twice.
Related calculators
For the reverse operation — finding how much a future amount is worth today — see the present value calculator. For a lump sum compounding at a stated annual rate with a chosen compounding frequency, the compound interest calculator covers that case directly. If you're paying down debt in equal installments instead of growing savings, the loan payment calculator uses the same annuity math to solve for the payment instead of the future value.
Frequently asked questions
- What is the future value formula?
- For a single lump-sum deposit, future value is FV = PV(1 + r)^n, where PV is the amount deposited today, r is the interest rate per period as a decimal (rate ÷ 100), and n is the number of periods. For a series of equal payments (an annuity), it's FV = PMT × ((1 + r)^n − 1)/r.
- How is future value different for a lump sum vs. an annuity?
- A lump sum is a single deposit made once, at the start, that then compounds for n periods. An annuity is a series of equal payments made every period, each of which compounds for a different number of remaining periods — the annuity formula sums all of those individually-compounded payments in one closed-form expression.
- What happens if I enter a 0% rate for an annuity?
- A 0% rate is a valid input, not an error. The annuity formula would divide by zero at r = 0, so this calculator falls back to the simple FV = PMT × n — the payments just add up with no interest earned.
- Why must the rate and periods use the same period unit?
- The rate here is per period, not per year — if you're depositing monthly, the rate must be the monthly rate and periods must be a count of months, not years. Mixing a monthly rate with a yearly period count (or vice versa) silently produces a wildly wrong answer.
- How is future value related to present value?
- Future value and present value are inverse operations built on the same compounding formula — FV multiplies by (1+r)^n to project a value forward in time, while present value divides by (1+r)^n to discount a future value back to today. See our present value calculator for the reverse direction.
- What's the difference between future value and compound interest?
- They share the same underlying formula for a lump sum — FV = PV(1+r)^n is identical to the compound interest total A = P(1+r/n)^(nt) when n = 1. Future value additionally covers the annuity case (recurring payments), which the compound interest calculator does not.
- Can the future value be less than the total contributed?
- Only if the rate is negative, which this calculator doesn't allow (rate must be 0 or more). With a rate of 0% or higher, future value is always greater than or equal to the total amount contributed — interest earned is never negative.