How this instrument works
Future value is what one sum becomes after growth has been applied a fixed number of times. Each period multiplies the balance by (1 + r), because interest joins that balance and then earns alongside it; applying such a multiplier n times over is exactly what raising it to power n means. Money never appears inside the exponent — only rate and period count do — so (1 + r)ⁿ is pure multiplication, indifferent to whether it acts on ten dollars or ten million.
That multiplier used to be looked up rather than computed. Compound amount factor tables, printed at back of actuarial and corporate finance texts, listed (1 + r)ⁿ to five decimals for every plausible rate and term, and a clerk did one multiplication by hand. Sensitivity lives in the exponent: at 7 percent, 10 periods multiply a stake by 1.9672, 20 periods by 3.8697, 30 periods by 7.6123. Doubling the horizon squares its factor rather than doubling it, which is why a long run delivers most of its gain in its final stretch.
Four things sit outside this arithmetic. Nothing is added along the way, since one deposit is left alone for every period — regular top-ups belong to an annuity calculation instead. Rate is held constant, which no market and few accounts deliver. Results come out nominal and pre-tax, so inflation and IRS treatment of interest or realised gains both bite afterwards. And running that identical factor backwards, dividing instead of multiplying, is what discounting means: present value and future value are one formula read in two directions.
- Enter Present value, $ — money in hand now, before growth of any kind is applied.
- Put one period's growth into Rate per period, %. Type 10 for ten percent, and check that your figure describes a period rather than a year, unless periods here are years.
- Set Number of periods to how many times that rate applies. Fractions are legitimate; so is zero, which returns your starting sum untouched.
- Read Future value. Divide it by Present value, $ to strip out money and see the growth factor on its own.
Worked example — ten percent for one period
Set Present value, $ to 1000, Rate per period, % to 10, and Number of periods to 1. One period elapses, so the multiplier lands once: 1 + 10 ⁄ 100 = 1.10, then 1000 × 1.10 = 1100. Future value reads $1,100 exactly — no rounding, no hidden convention, and no need for a machine to check it.
Small cases like that one earn their keep as calibration. Change Rate per period, % to 100, Number of periods to 2, and $1,000 becomes exactly $4,000: doubling twice quadruples, which compounding makes obvious where plain addition never would. Larger runs then deserve trust — leave defaults alone, $10,000 at 7 percent across 10 periods, and the readout gives $19,671.51, a hair short of doubling.
Questions
Does Rate per period mean an annual rate?
Only if your periods are years. Whatever percentage you type gets applied once per period, so both fields must run on one clock. A common wreck: entering 12 for a 12 percent annual quote beside 120 monthly periods. Twelve percent then applies one hundred twenty times over, turning $1,000 into roughly $806 million rather than $3,300.39. Monthly work needs a monthly rate — conventionally 12 ⁄ 12 = 1 — beside its monthly count.
How do I convert an annual rate into a rate per period?
Two defensible routes exist. Dividing follows disclosure convention: 10 percent per year, quoted nominally, becomes 10 ⁄ 12 = 0.8333 percent per month. Taking a root preserves an effective annual figure instead, since 1.10 raised to power 1⁄12 minus 1 gives 0.797 percent monthly, which compounds back over twelve months to precisely 10 percent. Division quietly overstates growth — 0.8333 percent monthly actually delivers 10.47 percent per year — so ask which basis your quote rests on before converting.
Can I use this for money I add every month?
No. One deposit only. Every dollar entered here is credited with all n periods of growth, so pooling planned contributions into Present value, $ inflates your result badly: cash arriving in period 29 of 30 earns one period, not thirty. Streams of equal payments need a future value of an annuity formula, which grows each payment for however long it personally sits.
What is present value, and how does it relate to this?
Same formula, read backwards. Future value multiplies by (1 + r)ⁿ; present value divides by it. A $10,000 payment promised in 5 years, discounted at 6 percent yearly, is worth 10,000 ⁄ 1.06⁵ = $7,472.58 today. That divisor is called a discount factor, and net present value work amounts to columns of them added up. Anyone weighing cash now against a larger sum later is using one of these two directions, whether they name it or not.
Why doesn't my portfolio match what this predicts?
Because constant rates are the fiction this arithmetic requires. Real returns arrive uneven, and unevenness costs money: +30 percent then −10 percent averages 10 percent per period, yet multiplies out to 1.30 × 0.90 = 1.17 against 1.21 where every period returns exactly 10. Fees come off before growth compounds, tax lands in years interest is credited or gains realised, and inflation erodes whatever survives. Read this figure as what a promised fixed rate would deliver, never as prophecy.
Are fractional or zero periods allowed?
Both. Zero returns your opening sum untouched, since anything raised to power zero equals 1 — a quick sanity check worth running on any sheet like this. Fractions interpolate smoothly: 1.07 raised to power 0.5 is 1.0344, so half a year at 7 percent lifts $10,000 to $10,344.08. Negative counts are blocked, as are negative starting sums; to run time backwards, divide by that factor instead of multiplying.
References
- SEC Investor.gov — investing basics and free tools
- Federal Reserve — H.15 selected interest rates
- IRS — About Publication 550, Investment Income and Expenses
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.