What is Future Value?
Future value (FV) is the amount a present sum or stream of payments will grow to at a specified future date, given an interest or growth rate. The single-sum formula is FV = PV x (1+r)^n. FV is the forward-looking counterpart to present value and the basis of retirement projections.
Detailed definition
Future value is the forward-looking sibling of present value. While PV asks 'what is tomorrow's money worth today,' FV asks 'what will today's money grow to by then.' The two are mirror images of the same compounding equation: PV is FV / (1+r)^n and FV is PV x (1+r)^n. FV is the standard tool for goal-based planning: how much will my $100,000 retirement contribution grow to in 30 years? How big will a 529 plan be by college? What is the future value of a 10-year US Treasury at maturity?
The basic single-lump-sum FV formula is FV = PV x (1+r)^n, which is just compound interest written forward. The annuity FV formula handles a stream of equal recurring payments: FV = PMT x (((1+r)^n - 1) / r). This is the right tool for periodic savings questions like 'if I save $500 a month for 30 years at 7%, what do I have?' Most financial calculators have a built-in TVM solver where you input PV, PMT, r, n, and a compounding-frequency setting to find FV; Excel's FV() and Google Sheets' FV() functions take the same five inputs.
The Rule of 72 gives a quick rule for doubling: at r% per year, money doubles in roughly 72 / r years. At 6% that is 12 years; at 8% it is 9 years; at 12% it is 6 years. The rule is a first-order Taylor expansion of FV = PV x 2 at r ln(2), and it lets you sanity-check FV figures in your head before reaching for a calculator. Pair it with the Rule of 114 (triples) and Rule of 144 (quadruples) for richer mental math.
FV calculations always require choosing a return assumption. For US equities the historical real return is about 7% per year over rolling 30-year periods, validated by Jeremy Siegel's data going back to 1802 and confirmed by 2026 long-run forecasts from major asset managers; for a mixed 60/40 portfolio it is closer to 5% real. Use real returns and then add expected inflation (US CPI averaged about 3% across the 2020s through 2025) back at the end, or use nominal returns directly and just stay consistent. Mixing nominal returns with real spending is the most common retirement-projection mistake, and the one that quietly understates required savings by 50% or more over a 30-year horizon.
Formula
FV = PV x (1 + r)^n (single sum) | FV = PMT x (((1+r)^n - 1) / r) (annuity)
- FV = Future value - amount at the end of n periods
- PV = Present value - amount today
- PMT = Periodic payment (positive for additions, negative for withdrawals)
- r = Interest or growth rate per period (decimal)
- n = Number of compounding periods
Worked example
Suppose you save $500 per month into a retirement account for 30 years at 7% annual return, compounded monthly.
- Monthly payment (PMT): $500
- Monthly rate (r): 0.07 / 12 = 0.005833
- Number of months (n): 30 x 12 = 360
- FV of annuity: PMT x (((1+r)^n - 1) / r): $500 x (((1.005833)^360 - 1) / 0.005833)
- Numerical result: $500 x 1,219.97 = $609,985
Related terms
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Frequently asked questions
What is future value?
Future value (FV) is the value that a current sum will grow to at a future date when applied at a given interest or growth rate. It is calculated from FV = PV x (1+r)^n for a lump sum or the annuity formula for recurring payments.
How is future value different from present value?
Future value compounds forward from today to a future date. Present value discounts backward from a future date to today. They are mirror images of the same time-value-of-money relationship.
How do I choose a return rate for FV projections?
Use a historically grounded long-run rate. US equities: ~7% real per year over 30+ years. Balanced 60/40: ~5% real. Bonds: ~2% real. Cash: ~0% real. Plus expected inflation if you want a nominal FV figure.
Should I use real or nominal returns for future value?
Either works as long as you stay consistent. If you use a real return (e.g., 5%), the FV is in today's purchasing power dollars. If you use a nominal return (e.g., 8%), the FV is in future inflated dollars. Mixing the two is the most common mistake.
What is the future value of an annuity?
It is the FV of a stream of equal periodic payments. The formula is FV = PMT x (((1+r)^n - 1) / r). A $500/month, 7%, 30-year annuity grows to about $610,000 from total contributions of $180,000.
Can future value be negative?
Only if you use a negative rate (deflation or guaranteed loss). In normal compounding, FV is always at least equal to PV for positive r. Negative FV usually indicates an input error or modelling a debt scenario.
How sensitive is FV to the rate assumption?
Very. A $500/month savings for 30 years grows to roughly $407,000 at 5%, $610,000 at 7%, and $930,000 at 9%. A two-point change in the assumed return shifts the 30-year endpoint by 50% or more. That sensitivity is why retirement plans should stress-test FV at three or four return levels instead of a single point estimate.
What is the future value of $1 over time at different rates?
At 4% per year, $1 doubles in roughly 18 years (Rule of 72: 72 / 4). At 6% it doubles in 12 years; at 8% in 9 years; at 10% in 7.2 years. Over 30 years, $1 grows to $3.24 at 4%, $5.74 at 6%, $10.06 at 8%, and $17.45 at 10%. Same time horizon, very different endpoints.