ReviewedEducational article · Updated Oct 2026
Key takeaways
- Money today can be invested, so it is worth more than the same amount later.
- Future value grows a sum forward; present value discounts a future sum back.
- The discount rate you choose changes the answer, so state it clearly.
- Loans, savings goals and investments all rely on this idea.
Would you rather have $10,000 today or $10,000 in ten years? Almost everyone chooses today, even ignoring inflation, because money in hand can be saved or invested. This preference, and the way we put numbers on it, is called the time value of money.
Future value
Future value asks: what will a sum today be worth later if it earns a given return? The formula is FV = PV × (1 + r)n, where PV is the present value, r is the rate per period and n is the number of periods.
Example: $10,000 invested at 5% a year for 5 years grows to 10,000 × 1.055 = $12,762.82.
Present value
Present value runs the process in reverse: what is a future sum worth today? The formula is PV = FV ÷ (1 + r)n, where r is called the discount rate.
Example: $10,000 received in 10 years, discounted at 5% a year, is worth 10,000 ÷ 1.0510 = $6,139.13 today. Put differently, $6,139 invested at 5% would become $10,000 in a decade.
Comparing money now with money later
Suppose you are offered $9,000 today or $10,000 in two years. Which is better depends on the rate you could earn elsewhere:
- At a 5% discount rate, $10,000 in two years is worth $9,070.29 today, slightly more than $9,000.
- At an 8% discount rate, it is worth $8,573.39 today, so taking the $9,000 is better.
The two offers are about equal at roughly 5.4%; above that rate, take the money now. The decision turns on the discount rate, not on the headline amounts.
Discounting is just compounding in reverse.
A stream of payments
Many financial products pay or cost a series of equal amounts: loan repayments, annuities, rent. The present value of $1,000 received at the end of each year for 10 years at 5% is $7,721.73, which is less than the $10,000 total because later payments are discounted more heavily. The loan payment formula used in the loan EMI calculator comes from exactly this idea: the payment is chosen so the present value of all repayments equals the amount borrowed.
Where you meet the idea in daily life
- Savings goals: how much per month to reach a target. See the math behind a savings goal.
- Loans: the payment is the present value equation solved for the instalment. See EMI and amortisation.
- Inflation: a dollar later buys less, which is another reason to prefer money now. See inflation and purchasing power.
- Doubling time: the Rule of 72 is a shortcut for future value.
Choosing a discount rate
There is no single correct rate. People use the return available on a safe alternative (like a savings account), the interest rate on debt they could repay, or their expected investment return. Using a higher rate makes the future look less valuable. Always state the rate you used so others can reproduce or challenge your result.
Common questions
Is this the same as compound interest?
It is the same mathematics. Compounding grows a present amount into a future one; discounting does the reverse. See how compound interest works.
Why not just add up the payments?
Because a dollar received later is worth less than one received now. Adding up nominal amounts ignores timing and can mislead.
Can I try these numbers?
Use the compound interest calculator for future values. The examples here are hypothetical and educational.
Common mistakes to avoid
- Leaving out the discount rate when comparing options.
- Mixing yearly rates with monthly periods in the formulas.
- Treating future money as equal to today’s money.
- Using an unrealistically high discount rate that makes the future look worthless.
Quick glossary
- Present value (PV)
- What a future amount is worth today.
- Future value (FV)
- What a present amount will be worth later.
- Discount rate
- The rate used to convert future amounts to today’s value.
- Annuity
- A series of equal payments at regular intervals.
Try it yourself
Compute the present value of $5,000 received in 8 years at 4% and at 7%. Notice how much the answer changes with the discount rate.
Further reading from official sources
These are general educational resources. Rules and figures differ by country, so look for your own country’s equivalent.
Related reading
This article is for general educational purposes only and is not financial advice. Examples use simplified, hypothetical numbers and ignore taxes, fees and personal circumstances. Consider speaking with a qualified professional before making financial decisions. See our full disclaimer.