Future Value Calculator

Background.

A future value calculator is the workhorse of time-value-of-money analysis: it tells you what a dollar invested today, or a stream of dollars deposited over time, will be worth at some specified horizon once interest has had a chance to compound. The concept is the foundation of corporate finance, retirement planning, bond pricing, lease valuation, and every back-of-the-envelope answer to the question "is this worth doing?" In Brealey, Myers and Allen's Principles of Corporate Finance — the standard MBA reference — the future-value identity is the very first equation introduced, because every other valuation model in finance reduces to discounting future cash flows back to the present or compounding present cash flows forward to the future.

This Quanta tool lets you do either direction. Enter a lump-sum present value, a recurring payment, an annual interest rate, a horizon in years, and a compounding frequency, and the calculator returns the future value, the total amount you actually contributed, the dollar amount of interest the math generated on top, and the effective annual rate that the chosen compounding frequency implies. It also inverts cleanly: switch the Solve For dropdown to Present Value to ask "how much do I need today to hit this target?", to Payment to ask "how much do I need to save each month?", or to Years to ask "how long until I get there?"

Two structural choices deserve emphasis up front because they trip up most users. First, payment timing. An ordinary annuity assumes every cash flow is paid at the end of its period — this is the convention for almost every savings account, mortgage, and retirement-plan deferral in the United States. An annuity-due, by contrast, assumes every payment is made at the beginning of the period — this is the convention for leases, insurance premiums, rent, and many subscription products. Annuity-due cash flows are worth more at the horizon by a factor of exactly (1 + i) per period, because each payment earns one extra period of interest. The dropdown gives you both.

Second, compounding frequency. The nominal rate you see advertised — 6% APR on a credit card, 5% APY on a savings account, 4% coupon on a bond — is not the same as the rate the money actually grows at once compounding is taken into account. The effective annual rate, EAR = (1 + r/m)^m − 1, where r is the nominal annual rate and m is the number of compounding periods per year, is always greater than or equal to r, and the gap widens as m increases. At 6% nominal, monthly compounding yields an EAR of 6.168%, daily compounding yields 6.183%, and continuous compounding yields the theoretical maximum of e^0.06 − 1 ≈ 6.184%. The calculator surfaces EAR as its own output so you can see exactly how much extra yield your chosen frequency buys you — and so you can compare two products advertised on different bases on an apples-to-apples footing.

We default the rate to 7% because that approximates the long-term real (inflation-adjusted) return of the U.S. equity market and is the figure used by the SEC's own investor-education materials. We default compounding to monthly because that is what the overwhelming majority of U.S. retail savings and investment products actually use internally, regardless of how the yield is quoted on the marketing page. And we default payment timing to end-of-period because that is the conservative assumption that matches every standard textbook annuity formula. Use this calculator to project retirement balances, validate bond and CD yields, size up a savings goal, price a fixed-term lease, or pressure-test the time value of any cash-flow stream you are evaluating. Below the widget you will find the full formula, a worked example with the canonical $1,000-at-7%-for-10-years lump-sum problem alongside a 30-year $200-per-month savings annuity, eight long-tail FAQs that answer the questions students and practitioners actually ask, and primary-source citations to Brealey/Myers/Allen, Bodie/Kane/Marcus, the CFA Institute's TVM curriculum, the SEC's Investor.gov, and Mishkin's Money, Banking and Financial Markets — the five most widely assigned references in the field.

What is future value calculator?

Future value (FV) is the amount that a current sum of money, or a series of cash flows, will grow to at a specified date in the future, given an assumed rate of return and a defined compounding frequency. It is the forward-looking complement of present value (PV), which discounts future cash flows back to today. The two are linked by the same identity: FV = PV × (1 + i)^n. For a single lump sum that earns interest with no further contributions, FV is the lump sum compounded forward. For a stream of equal payments — an annuity — FV is the sum of each payment compounded forward to the horizon date; whether the payments arrive at the end of each period (ordinary annuity) or the beginning (annuity-due) shifts the answer by a multiplicative factor of (1 + i). Future value sits at the foundation of retirement planning ("what will my 401(k) be worth at 65?"), bond pricing (the maturity value used to price a zero-coupon bond), savings goals ("how much will my $300/month grow to in 20 years?"), and corporate capital budgeting (the terminal value at the end of a forecast period). Because the formula is exponential rather than linear, small changes in the interest rate, the horizon, or the contribution amount produce disproportionate changes in the ending balance — which is why the time value of money is sometimes called the most important concept in finance.

How to use this calculator.

1. 01Choose Solve For. Leave it on Future Value for a standard forward projection. Switch to Present Value, Payment, or Years if you have a target FV and want to back out one of the other variables.
2. 02Enter the Present Value — the lump sum invested today. Set this to 0 if you are starting from scratch and rely entirely on periodic payments.
3. 03Enter the Periodic Payment. This is the cash flow paid each compounding period. Use 0 for a pure lump-sum problem. If you are saving $200/month and compounding monthly, enter 200. If you are compounding annually but saving $200/month, enter 2,400 (the per-period contribution).
4. 04Set the Annual Interest Rate as a nominal APR. The calculator divides by the compounding frequency to get the per-period rate.
5. 05Enter Years — the full investment horizon. For a 35-year-old retiring at 65, enter 30. (This field is ignored when Solve For = Years.)
6. 06Choose Compounding Frequency. Monthly is the most common real-world default for savings, brokerage, and retirement accounts. Annual is typical for fixed-coupon bonds. Daily is typical for high-yield savings accounts.
7. 07Choose Payment Timing. End of Period is the ordinary-annuity convention used for almost every U.S. savings and retirement context. Beginning of Period is the annuity-due convention used for leases, rent, and insurance premiums.
8. 08If you set Solve For to anything other than Future Value, enter the Target Future Value the calculator should solve back to.
9. 09Read the four outputs: Future Value (the ending balance), Total Contributions (your out-of-pocket cash), Total Interest Earned (the compounded growth), and Effective Annual Rate (the true annualized yield implied by your nominal rate and compounding frequency).

The formula.

The calculator implements the canonical time-value-of-money identity used in every corporate-finance textbook. Let i = r / m be the per-period interest rate, where r is the annual nominal rate (as a decimal) and m is the number of compounding periods per year. Let n = years × m be the total number of compounding periods. Then the future value of a lump-sum present value PV is FV_lump = PV × (1 + i)^n. The future value of an ordinary annuity — equal payments PMT made at the end of each period — is FV_annuity = PMT × [((1 + i)^n − 1) / i]. For an annuity-due (payments made at the beginning of each period), every cash flow earns one extra period of interest, so the annuity formula is multiplied by (1 + i): FV_annuity_due = PMT × [((1 + i)^n − 1) / i] × (1 + i). Combined: FV_total = PV × (1 + i)^n + PMT × [((1 + i)^n − 1) / i] × due_factor, where due_factor = 1 for end-of-period payments and (1 + i) for beginning-of-period payments. When i = 0 the annuity term degenerates to PMT × n × due_factor, so a zero-rate scenario still returns a sensible number rather than a divide-by-zero. The effective annual rate — the true compounded yield once compounding frequency is taken into account — is EAR = (1 + r/m)^m − 1, and is reported as its own output. The inverse solvers rearrange the same identity: PV = (FV − FV_annuity) / (1 + i)^n; PMT = (FV − PV × (1 + i)^n) × i / ((1 + i)^n − 1) / due_factor; n = ln((FV × i + PMT × due_f) / (PV × i + PMT × due_f)) / ln(1 + i), with the result divided by m to convert periods back to years. All math is executed in arbitrary-precision Decimal arithmetic so that 360-month and 480-month horizons do not accumulate floating-point error.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Brealey, R.A., Myers, S.C., and Allen, F. — Principles of Corporate Finance, 13th edition. Chapter 2 introduces the future value identity FV = PV × (1 + r)^t and develops the annuity formulas used in this calculator.
2. [2]Bodie, Z., Kane, A., and Marcus, A.J. — Investments, 12th edition. §5 covers the time value of money, effective vs. nominal rates, and annuity valuation as applied to portfolio choice.
3. [3]CFA Institute — Quantitative Methods curriculum, Time Value of Money reading. Defines FV/PV/PMT/n/i framework and the inverse solvers used at the Level I exam.
4. [4]U.S. Securities and Exchange Commission, Investor.gov — Compound Interest Calculator and accompanying investor-education materials on future value and the time value of money.
5. [5]Mishkin, F.S. — The Economics of Money, Banking, and Financial Markets, 13th edition. Chapter 4 derives the future and present value formulas and motivates the role of compounding frequency in fixed-income pricing.
6. [6]Consumer Financial Protection Bureau — Regulation Z (Truth in Lending) and Regulation DD (Truth in Savings), which mandate APR and APY disclosure so consumers can compare nominal-rate products on an effective-annual-rate basis.