The time value of money, explained simply
A dollar you have today is worth more than a dollar you get later, because today's dollar can be invested and grow. That one idea prices every loan, every savings account and every retirement plan, and it decides how much your money becomes.
Updated October 20, 2026 · 7 min read · Plain math, no product pitches
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What the time value of money means
Offer someone $1,000 today or $1,000 in five years and almost everyone takes it today. That instinct has a name: the time value of money. Money in your hand now can be put to work, so it is worth more than the same number of dollars arriving later.
The idea sounds obvious, but it has a precise, useful form. Given a rate, you can say exactly how much $1,000 today becomes in five years, and exactly how much $1,000 in five years is worth today. Banks, lenders, pension funds and card companies run on this math. Most people never see it written down, which is why it so often works against them instead of for them.
Why a dollar today is worth more than a dollar later
Three separate reasons, and they stack:
- It can earn something. A dollar invested today earns interest or returns, and next year that growth earns more growth. Waiting means giving that up. Economists call it the opportunity cost.
- Prices rise. With inflation around 3% a year, $1,000 in five years buys what about $863 buys today.
- Later is less certain. A promise to pay you later might not be kept in full. The less sure the payment, the less it is worth now.
All three point the same way: get money sooner, pay money later, and when you compare the two, put them on the same date first.
Interest, compounding and return: how they fit together
Three ideas sit underneath the time value of money. Each builds on the one before.
- Simple interest is paid only on the original amount. $10,000 at 6% simple interest earns $600 every year, so after 10 years you have $16,000. The money grows in a straight line.
- Compound interest is paid on the original amount plus the interest already earned. The same $10,000 at 6% compounded yearly has $17,908 after 10 years, and the gap keeps widening: after 30 years it is $28,000 simple against $57,435 compounded. The money grows on a curve.
- Rate of return is the broader version: everything your money earns from any source, interest, dividends and price changes, as a percentage. Investments do not pay a fixed rate; their return changes every year, so you measure it after the fact and plan with a cautious average.
The time value of money takes whichever rate applies (a loan’s interest rate, a savings yield, an expected return) and uses compounding to move money forward or back in time. Get the rate right and the rest is arithmetic.
Simple vs compound interest, side by side →With a year-by-year calculator and what APR and APY really mean.The two formulas behind it
Every time value of money problem moves money along a timeline, either forward (compounding) or back (discounting). One formula does each.
Future value: what money today grows into
- FV
- future value, what you end with
- PV
- present value, what you start with
- r
- rate per period, as a decimal (5% = 0.05)
- n
- number of periods
Present value: what future money is worth today
Most real problems add a regular deposit or payment (a monthly savings amount, a loan payment). That adds one more term, covered step by step with every variation in the formula guide.
The time value of money formulas, step by step →Future value, present value, annuities, solving for the rate or the years, and the matching spreadsheet functions.Time value of money calculator
Pick what you want to find. Fill in the other four and the answer updates as you type, with the formula and your numbers shown underneath.
Time value of money calculator
Solve for future value, present value, the deposit, the rate or the number of years.
Solve for
Future value
$144,572.72
Starting with $10,000 and adding $200 a month at 7% for 20 years grows to $144,573.
You put in
$58,000
Growth
$86,573
60% of the total
FV = PV(1 + i)n + PMT × [((1 + i)n − 1) ÷ i]
i = 7% ÷ 12 = 0.5833% a month; n = 20 × 12 = 240 months
$144,572.72 = $10,000(1 + 0.005833)240 + $200.00 × [((1 + 0.005833)240 − 1) ÷ 0.005833]
Time and rate: the two levers
In FV = PV × (1 + r)n, the rate sits inside the brackets and time sits in the exponent. Both matter, and they multiply each other. Here is $10,000 left alone, compounded once a year:
| Yearly rate | 10 years | 20 years | 30 years | 40 years |
|---|---|---|---|---|
| 4% | $14,802 | $21,911 | $32,434 | $48,010 |
| 7% | $19,672 | $38,697 | $76,123 | $149,745 |
| 10% | $25,937 | $67,275 | $174,494 | $452,593 |
Two things jump out:
- The last decade does the most. At 7%, the money grows about $9,700 in the first ten years and about $73,600 in the fourth. Same rate, same money; the difference is what it has already grown into.
- A few points of rate become a multiple over time. 10% is not 43% more than 7%; over 40 years it is three times the money. That is why fees and returns deserve real attention.
It works against you too
The same math runs in reverse on debt. A credit card balance at 24% a year, compounded monthly, grows from $5,000 to $6,341 in one year if nothing is paid. That is the time value of money working for the card company: you got the goods sooner, and you pay for the privilege at a rate few investments ever earn.
Using it for real decisions
A lump sum or payments over time
Pensions, lottery wins, legal settlements and some insurance payouts offer a choice: one amount now, or a series of payments. Adding up the payments is the wrong comparison. Bring each payment back to today and add those.
Paying now or paying later
Interest-free time is worth money. A bill paid by card on day 1 and paid off in full on day 50 leaves your cash in savings for those 50 days. A 0% offer for 12 months on a purchase you were going to make anyway is a small loan at no cost, as long as it is paid in full before the rate jumps.
Saving now or saving later
Every year you delay is a year cut off the end of the timeline, which is where the biggest growth happens. The cheapest way to have more money later is usually not a higher rate; it is an earlier start.
Small amounts, long times
Take $3.50 a day, the price of a coffee: about $106 a month. Invested at 7% a year (a cautious long-run planning figure for stocks, before inflation), it grows like this:
| After | You put in | It grows to |
|---|---|---|
| 10 years | $12,775 | $18,426 |
| 20 years | $25,550 | $55,457 |
| 30 years | $38,325 | $129,876 |
| 40 years | $51,100 | $279,433 |
That is real money from a small habit, and most of it is growth, not deposits. It is also not a million dollars: claims that a few dollars a day becomes $1 million in ten years need returns no one can count on. Honest math is more useful than exciting math, because you can plan on it.
The bigger lever for most people is finding larger amounts that are already leaking: interest on a card balance, unused subscriptions, fees, and card rewards left unclaimed on bills you pay anyway. The leak check finds the first group and the bill router the second.
Common mistakes
- Adding up future payments as if they were today’s dollars. $750,000 paid over 25 years is not worth $750,000.
- Mixing periods. With monthly deposits, use the monthly rate (yearly rate ÷ 12) and the number of months. A yearly rate with a monthly count of periods gives nonsense.
- Using an optimistic rate. The rate is the most sensitive input. Plan with a cautious one and treat anything better as a bonus.
- Forgetting inflation. $1 million in 30 years buys what about $412,000 buys today at 3% inflation. Say which kind of dollars an answer is in.
- Ignoring fees. A 1% yearly fee comes straight off the rate, and over decades it takes a large share of the growth.
Questions people ask
What is the time value of money in simple terms?
Money you have now is worth more than the same amount later, because money you have now can earn interest or returns in the meantime. $1,000 today invested at 5% a year is $1,276 in five years, so $1,000 promised five years from now is worth less than $1,000 today.
Why is the time value of money important?
It is how you compare money at different times: a lump sum against monthly payments, paying now against paying later, saving now against saving in ten years. It also shows why starting early matters so much, since time is the part of the formula that grows fastest.
What is the time value of money formula?
Future value is FV = PV × (1 + r)^n, where PV is the money today, r is the rate per period and n is the number of periods. Turned around, present value is PV = FV ÷ (1 + r)^n. With regular deposits, add PMT × [((1 + r)^n − 1) ÷ r] to the future value.
What are the five time value of money variables?
Present value (PV), future value (FV), payment per period (PMT), interest rate per period (I/Y or r) and number of periods (N). Know any four and you can solve for the fifth, which is what financial calculators and spreadsheet functions like FV, PV, PMT, RATE and NPER do.
Is the time value of money the same as compound interest?
Compound interest is the engine; the time value of money is the idea built on it. Compounding takes money forward in time (what will this grow into?), and discounting takes it back (what is that future amount worth today?). Both use the same rate and the same exponent.
Does the time value of money include inflation?
Inflation is one of the reasons money loses value over time, but the formulas only include it if you use a rate that accounts for it. Use a nominal rate to get future dollars, or a real (after-inflation) rate to get the answer in today's dollars.
What rate should I use?
Use the rate you could realistically earn on the money instead, at a similar level of risk. For a savings account, its yield. For a long-term stock investment, a cautious planning figure such as 6% to 7% a year before inflation. For paying off debt, the debt's interest rate.