📈 Future Value Calculator
Work out the future value of a lump sum invested today, a series of regular payments (an annuity), or both together — using the time-value-of-money formula FV = PV × (1 + r/n)^(nt). The calculator shows the formula with your own numbers substituted, splits the result into contributions versus interest earned, supports ordinary and annuity-due timing, and converts your nominal rate to an effective annual rate.
FV = PV × (1 + r/n)nt for the lump sum, plus the annuity formula for the payment stream. It shows the formula with your own numbers substituted, splits your total into contributions vs interest earned, and converts your nominal rate to an effective annual rate.
Methodology & Sources
The future value of a single lump sum is FV = PV × (1 + r/n)n×t, where PV is the present value invested today, r is the nominal annual rate, n is the number of compounding periods per year, and t is the number of years. Increasing n (compounding more often) raises the future value, but with sharply diminishing returns — the jump from annual to monthly is far larger than the jump from monthly to daily, and the gap from daily to continuous compounding is tiny.
The future value of a series of equal payments (an annuity) is FV = PMT × [((1 + i)N − 1) / i], where i is the periodic rate (annualRate ÷ contributionFrequency) and N is the total number of payments (contributionFrequency × years). This is the ordinary annuity formula, which assumes each payment arrives at the end of its period. If you contribute at the start of each period instead (an annuity-due), every payment earns one extra period of compounding, so the result is multiplied by (1 + i) — always slightly larger. When the rate is exactly 0%, the annuity formula would divide by zero, so the calculator falls back to PMT × N (you simply get back what you paid in).
The lump sum and the payment stream are modelled with their own compounding frequencies so each is internally correct even when the two differ (e.g. a deposit that compounds daily alongside monthly contributions). The effective annual rate (EAR) is derived from the nominal rate and the lump-sum compounding frequency as ((1 + r/n)n − 1) × 100 — it is the rate that, compounded once a year, produces the same growth as your nominal rate compounded n times. A 7% nominal rate compounded monthly is a 7.229% effective rate; this is the number to compare across accounts that quote different compounding conventions.
This calculator is a gross time-value-of-money tool and intentionally does not model: taxes on growth or contributions, inflation (use the Inflation Impact Calculator to see future value in today’s purchasing power), variable or non-constant returns, fees, or contributions that grow over time. For consumer-savings framing of the same compounding math, see the Compound Interest Calculator; for a full investment-growth projection with a contribution schedule, see the Investment Growth Calculator.
- Future value concept & formula: Investopedia — Future Value (FV)
- Time value of money fundamentals: CFA Institute — Quantitative Methods & Time Value of Money
- Annuity future value: Investopedia — Future Value of an Annuity
Last verified: May 2026.
Frequently Asked Questions
FV = PV × (1 + r/n)nt, where PV is the present value, r is the annual rate (as a decimal), n is the number of times interest compounds per year, and t is the number of years. So $5,000 at 6% compounded quarterly for 8 years is 5000 × (1 + 0.06/4)4×8 = 5000 × 1.01532 ≈ $8,051. For a stream of equal payments, you add the annuity future value: FV = PMT × [((1 + i)N − 1) / i], with i the periodic rate and N the total number of payments. The calculator above shows the lump-sum formula with your own numbers substituted in the “The formula” box, and adds the annuity component automatically when you enter a recurring payment.(1 + r/n)nt. Present value moves money backward in time: how much do I need to invest today to have $20,000 in 10 years? You divide by the same growth factor (this is called discounting). FV compounds, PV discounts, and they invert each other — PV = FV / (1 + r/n)nt. Use future value when you know what you can invest now and want to project the outcome; use present value when you know the target amount and want to back out today’s required deposit, or when you want to value a future cash flow (like a bond payment or a pension) in today’s money.(1 + i) where i is the periodic rate. As a rule of thumb: rent, insurance premiums, and lease payments are annuities-due (you pay at the start of the month). Loan repayments, bond coupons, and most savings contributions made “at month end” are ordinary annuities. For a 401(k) or IRA where you contribute from each paycheck, end-of-period (ordinary) is the conventional and conservative choice. If you front-load contributions on the 1st, switch to beginning to capture the extra compounding — over decades it adds up.FV = PV × ert), which for this example is about $20,138 — essentially indistinguishable from daily. The practical takeaway: compounding frequency is real but small. Don’t chase a “daily compounding” account at a lower headline rate over a “monthly compounding” account at a higher rate — compare the effective annual rate instead, which normalises for compounding.((1 + r/n)n − 1). For 7% nominal compounded monthly the EAR is 7.229%, because each month’s interest itself earns interest for the rest of the year. The more frequent the compounding, the larger the gap between nominal and effective. EAR is the apples-to-apples number for comparing accounts that compound on different schedules — a 7% monthly account (7.229% EAR) beats a 7.1% annual account (7.1% EAR). In the UK this effective figure is broadly the AER on savings; on loans the analogous concept is the APR.How to use this calculator
Takes about 1 minute.
- Enter the present value (a lump sum invested today) — set it to 0 if you only want the annuity
- Enter the recurring payment per period — set it to 0 for a lump-sum-only calculation
- Set the nominal annual interest rate and the number of years
- Choose the compounding frequency for the lump sum and the contribution frequency for the payments
- Pick payment timing: end of period (ordinary annuity) or beginning (annuity-due)
- Read off the total future value, the lump-sum and annuity components, total contributions vs interest earned, and the effective annual rate
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Key concepts
Future value is the forward-looking core of the time value of money (TVM) — what a sum today, or a stream of payments, becomes after a period of compounding. The foundational idea is that money has a time dimension: a dollar in hand today is worth more than a dollar promised next year, because today’s dollar can be invested to earn a return. Future value quantifies that growth. For a single lump sum the formula is FV = PV × (1 + r/n)n×t, where PV is the present value, r the nominal annual rate, n the number of compounding periods per year, and t the number of years. A $10,000 deposit at 7% compounded monthly becomes about $20,097 in ten years — the original principal plus roughly $10,097 of compounded growth, more than doubling the money without adding a cent.
Future value and present value are inverses of each other. Where future value multiplies by the growth factor to move money forward in time, present value divides by the same factor to move money backward — a process called discounting. PV = FV / (1 + r/n)nt. The two operations are mirror images: ask “what will $10,000 be worth in 10 years?” and you compute future value; ask “how much must I invest today to have $20,000 in 10 years?” and you compute present value. This FV/PV duality underpins almost every quantitative decision in finance: valuing bonds (the price is the present value of future coupons plus principal), capital budgeting (net present value discounts a project’s future cash flows), pension valuation, and loan amortisation. Mastering the future-value direction first makes the discounting direction intuitive, because it is simply the same equation solved for the other variable.
When the money arrives as a series of equal payments rather than a single lump, you use the annuity future-value formula. An annuity is any sequence of equal cash flows at regular intervals — monthly 401(k) contributions, an annual ISA top-up, a fixed pension deposit. Its future value is FV = PMT × [((1 + i)N − 1) / i], where i is the periodic rate (the annual rate divided by the number of payments per year) and N is the total number of payments. The bracketed term is the annuity future-value factor, and it is derived by summing a geometric series: each payment compounds for a different number of periods (the first payment compounds the longest, the last barely at all), and the closed-form expression collapses that sum into a single factor. A subtle but important variant is timing: the standard formula assumes payments at the end of each period (an ordinary annuity). If instead you pay at the start of each period (an annuity-due, as with rent or insurance), every cash flow earns one extra period of compounding, so you multiply the result by (1 + i) — making an annuity-due always worth marginally more than the otherwise-identical ordinary annuity.
Compounding frequency matters, but less than people expect. The more often interest is added to the balance, the more often that interest itself earns interest, so a higher n produces a higher future value — but with steeply diminishing returns. At 7% over ten years, $10,000 grows to about $19,672 with annual compounding, $20,097 with monthly, and $20,136 with daily; the mathematical ceiling of continuous compounding (FV = PV × ert) is about $20,138. The first step up (annual to monthly) is worth roughly ten times the second (monthly to daily). The honest way to compare accounts that compound differently is the effective annual rate (EAR), ((1 + r/n)n − 1), which restates any nominal-plus-frequency combination as a single once-a-year rate. A 7% nominal rate compounded monthly is a 7.229% effective rate; comparing EARs prevents a lower headline rate with daily compounding from looking better than it is.
Real-world future-value applications span personal finance and corporate finance alike. In retirement planning, FV combines a starting balance (lump sum) with ongoing contributions (an annuity) to project a pot decades out — and over a 30-to-40-year horizon the compounded interest typically dwarfs the contributions, which is the entire argument for starting early. In education funding, parents work out what regular deposits will accumulate to by the time a child reaches university. In bond pricing, the future (maturity) value and coupon stream are discounted back to a present price. In capital budgeting, future cash flows from a project are projected and compared. Two limitations are worth holding in mind: a future-value figure is nominal, so it ignores inflation — $20,000 in 20 years buys far less than $20,000 today, which is why a real-purchasing-power adjustment matters — and it assumes a constant rate, whereas real returns vary year to year. Treat the output as a disciplined projection, not a guarantee, and pair it with an inflation adjustment and a range of rate assumptions for serious planning.
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