In the formula FV = PV × (1 + r)^n, what does FV represent?
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Finance · Foundations
Future Value
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In 30 seconds
Future value is what an amount of money today grows to by a future date when it earns a Return The gain an investment produces over time, usually expressed as a percentage of the amount invested. Full entry →. Put $200 in an account paying 6% a year, and after three years it holds $238.20: the original $200 plus everything the interest earned. The formula is FV = PV × (1 + rate)^years — each year the balance earns more on top of what it already has. Future value turns a savings or investment decision into a number you can plan around, remembering the number is a Projection A calculated estimate of a future amount based on stated assumptions, such as a rate that may not hold. Full entry →, not a promise.
Why this matters
Future value answers the question behind almost every money decision that involves time: what will this amount become? Set a savings goal and future value tells you whether your starting amount and expected rate get you there. Compare two investments and future value puts different rates and horizons on the same scale. Borrow money and the same math shows what the debt costs by the time it is repaid. The idea also underpins the rest of finance — present value, compound interest, and valuation all lean on this growth relationship — so mastering one formula opens the door to the others.
The college version
What future value is
Future value (FV) The amount a sum of money today is expected to be worth at a future date when it earns a stated rate of return. Full entry → is the amount an investment made today will be worth at a future time, given a rate. The working definition used by OpenStax's Principles of Finance: future value refers to how a specific amount of money today can have greater value tomorrow. The phrase matters as much as the math. Future value is not a different pile of money; it is the same money, plus everything it earned while it waited. That is why the definition always names three things at once: the starting amount, the rate, and the time. Change any one of them and the future value changes with it. A one-year horizon makes this easy to see: $1,000 at 4% becomes $1,040, and the $40 is simply the first year's interest added to the starting balance.
The growth idea and the one formula
Money grows because it can earn. Deposited in an interest-bearing account or invested in something that produces returns, a sum of money grows over time as interest accrues or returns are realized. The growth idea is simple, but the arithmetic repeats: each year the balance is multiplied by one plus the rate. Write that as a single line and you get the formula taught in every finance course: FV = PV × (1 + rate)^years. PV is the present value, the amount today; rate is the return per year, written as a decimal; years is how long the money grows; and the superscript means the factor is applied once for every year. For $200 at 6% for three years, the calculation is $200 × 1.06 × 1.06 × 1.06, which comes to $238.20. One amount, one rate, one time span — one answer.
Compounding: growth on growth (a preview)
Notice what happened in the three-year example. Year one earned $12.00 on the $200. Year two earned $12.72, because it was 6% of $212.00, not of $200. Year three earned $13.48, 6% of $224.72. The interest kept growing because the balance it was computed on kept growing. That is Compounding The process in which interest earned in one period earns its own interest in later periods, so the balance grows on top of itself. Full entry →: interest earning interest, growth building on growth. Compounding is the engine of future value — the reason the balance does not grow in a straight line but in a curve that steepens with time and with rate. A full treatment of compound interest, including how often interest is credited, belongs to its own topic; here the important idea is that the formula already contains it, because the factor (1 + rate) is applied to the running balance each year.
Future value and present value: the pair
Future value has a mirror image. If future value asks what today's money grows to, present value asks what a future amount is worth today. OpenStax puts it plainly: compounding is the process that carries a present value forward to a future value, while discounting carries a future value back to today's dollars — the exact opposite of compounding. The two are the same relationship read in different directions, and the formulas are inverses of each other. Present value is covered fully in its own lesson; this one uses it in two places only: as the starting amount in the future-value formula, and as the comparison point that makes future amounts meaningful in today's terms.
Why it matters — and the honest framing
Future value shows up wherever money waits. A saver uses it to check whether a deposit at a stated rate will hit a goal by a target date. An investor uses it to compare two opportunities with different rates and horizons on a common scale. A borrower meets it from the other side, because the same rate that pays a lender is charged to the borrower, and the amount owed grows by the same math. The honest framing: a future value is a projection, not a promise. The calculation is exact, but it is exact about an assumption — the rate. Rates change, returns vary, and investments can lose money, so the realized amount can land anywhere relative to the projection. Use future value as a planning number, and treat the gap between projection and reality as part of the plan. A projection that accounts for that gap is still the best tool we have for seeing what money can become.
Eli explains
The same idea, in plain words
Explain it like I’m 10
Future value answers one question: if I set this money aside and it earns money while I wait, how much will I have when the waiting is over? Start with any amount. Add the return it earns in the first year, and that total earns again in the second year, and so on. The only inputs are how much you start with, how fast the money grows each year, and how many years it grows. The formula packs all of that into one line: the starting amount, times one plus the rate, repeated once for every year.
Picture it like this
Think of future value as a snowball rolling downhill. The snowball is your starting money, and each year of rolling packs on another layer of snow — the return. A bigger snowball picks up even more snow on the next roll, because the new layer is a percentage of a larger ball. The longer the hill, and the sticker the snow, the bigger the ball at the bottom.
Where the picture stops working
A snowball always grows; money does not have to. A rate below zero, an investment that loses value, or returns that never arrive make the future amount smaller than the starting one. The formula also assumes the same rate holds every year, which real markets do not guarantee.
Worked example
Mara puts $200 into a certificate of deposit that pays 6% interest each year, compounded annually, and leaves it untouched for three years. Year one: $200 × 0.06 = $12.00 in interest, so the balance becomes $212.00. Year two: $212.00 × 0.06 = $12.72 in interest, so the balance becomes $224.72. Year three: $224.72 × 0.06 = $13.48 in interest, so the balance becomes $238.20. The same result falls out of the formula: FV = $200 × (1.06)^3 = $200 × 1.191016 = $238.20. Of the $38.20 of growth, $36.00 is interest on the original $200 and the remaining $2.20 is interest earned on interest.
Key takeaway
Future value is what money today grows to when it earns a return: FV = PV × (1 + rate)^years. Use it to set goals and compare options — and treat it as a projection built on an assumed rate, not a promise of what will arrive.
Quick check
3 questions here, of 5 in this lesson’s practice set. Answers stay hidden until you check.
Which of the following is NOT one of the three inputs needed to compute a future value?
Choose an answer, then check it.
You deposit $300 in an account that earns 5% interest per year, compounded annually, and leave it untouched for two years. What is the future value of your deposit?
Choose an answer, then check it.
Study tools & related lessonsYou’ll learn to · Common mistakes · Easily confused · Key vocabulary · Related
You’ll learn to
- Define future value as the amount an investment made today is expected to be worth at a future time given a rate of return.
- Explain why money grows over time when it earns returns.
- Apply the formula FV = PV × (1 + rate)^years to compute the future value of a single amount.
- Analyze how compounding makes growth accelerate as the time horizon or the rate increases.
- Distinguish future value (what today's money grows to) from present value (what future money is worth today).
- Evaluate what a future-value projection can and cannot promise.
Common mistakes
Adding the same interest every year instead of compounding it, so three years at 6% on $200 becomes $200 + 3 × $12 = $236.00.
Interest is earned on the whole balance, not just the original $200. Compounding gives $238.20; the extra $2.20 is the interest earned on earlier interest.
Using the rate as a whole number instead of a decimal, as in $200 × (1 + 6)^3.
Convert the percentage first: 6% is 0.06, so the growth factor is 1.06. Anything else makes the factor absurdly large.
Raising the starting amount to a power along with the factor, like $200^3 × 1.06.
Only the (1 + rate) factor is raised to the number of years. The starting amount is multiplied by that factor, not powered.
Reading the result as a guarantee of what the account will hold.
Future value is a projection built on the assumed rate. If the rate changes or the investment loses value, the realized amount will differ.
Easily confused
Future value vs. Present value
Future value moves today's money forward in time; present value brings future money back to today. They are the same growth relationship read in opposite directions.
Simple growth vs. Compounded growth
Simple growth pays on the original amount every year; compounded growth pays on the running balance, so the growth itself grows.
Projection vs. Promise
A projection states what a future value will be if the assumed rate holds; a promise guarantees the amount regardless of what actually happens.
Key vocabulary
- Future value (FV)
- The amount a sum of money today is expected to be worth at a future date when it earns a stated rate of return.
- Present value (PV)
- The amount of money today that a future sum is worth given a rate of return; the starting amount in a future-value calculation.
- Interest rate
- The percentage of an amount that is earned by the lender of funds or charged to the borrower over a period, expressed as a decimal in the future-value formula.
- Compounding
- The process in which interest earned in one period earns its own interest in later periods, so the balance grows on top of itself.
- Principal
- The original amount deposited or invested before any interest is earned.
- Return
- The gain an investment produces over time, usually expressed as a percentage of the amount invested.
- Growth rate
- The annual percentage increase applied to savings or an investment, used as the rate in the future-value formula.
- Projection
- A calculated estimate of a future amount based on stated assumptions, such as a rate that may not hold.
Sources & references
- Principles of Finance, Section 7.2: Time Value of Money (TVM) Basics — OpenStax, Rice University
- Principles of Finance, Section 7.4: Applications of TVM in Finance — OpenStax, Rice University
- Time Value of Money – How to Calculate the PV and FV of Money — Corporate Finance Institute (CFI)
- Compound Interest Calculator — U.S. Securities and Exchange Commission (Investor.gov)
EliExplains lessons are original prose written from the open, credible references above. See Copyright & Licensing.
Researched 2026-08-21
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