Future value and present value meaning
Future value (FV) is what a sum of money held today will be worth at a later date after it earns interest. Present value (PV) is the reverse: what a sum due at a later date is worth today, after you take out the interest it could have earned in the meantime.
Both rest on the time value of money. A rupee today is worth more than a rupee later, because today's rupee can earn interest. The process of going from future to present is called discounting. The process of going from present to future is called compounding.
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Future value formula and present value formula
Let:
- r be the interest rate per period, written as a decimal
- n be the number of periods
- G be the growth factor per period: what each rupee becomes after a period at rate r, meaning the rupee itself plus r of interest
Then:
- Future value formula: FV = PV × Gⁿ
- Present value formula: PV = FV ÷ Gⁿ
The ratio PV ÷ FV is the discount factor. When rates are higher or the wait is longer, the discount factor is smaller.
Worked example
This is a hypothetical case. Suppose Sana is promised an amount in some years' time, and the rate she could earn instead matches the policy rate in the latest State Bank of Pakistan (SBP) decision. The SBP announcement reads: SBP policy rate raised by 50 bps to 12% with effect from 27.10.2026 (MPC).
- To find the future value of money she holds today, she multiplies it by the growth factor once for each year.
- To find the present value of the promised amount, she divides it by the same factor once for each year.
The present value always comes out below the promised amount when the rate is positive. To get exact figures, enter your own amount, rate and number of years in the tools on the calculators page.
Where the terms appear
- Bond prices. A bond's price is the present value of its coupons and its face value. When rates rise, prices fall.
- News on rate decisions. A change of a few basis points in the policy rate changes the discount rate behind loans, deposits and bond yields.
- Loans and savings. Repayment schedules (amortization) and deposit projections are built on these formulas. See Saving, Investing, Loans.
- FX forwards and swaps. Forward points and overnight swap fees reflect interest differences between two currencies, which is a time-value calculation (covered interest parity).
Trading platforms such as MetaTrader do not show FV or PV directly. They do charge or pay swaps based on the same idea. Keep in mind that leveraged CFD and forex positions can lose money fast, so swap costs are only part of the risk.
Precise definition and edge cases
- Compounding frequency. If interest is added m times per year, use r ÷ m per sub-period and n × m sub-periods. With continuous compounding, PV = FV × e^(−r × n).
- Changing rates. If the rate differs each period, multiply the separate growth factors. Do not use a single average rate.
- Nominal and real values. Discounting at a nominal rate gives rupees of that date. To compare purchasing power, use a real rate, which is the nominal rate adjusted for inflation (see deflation).
- Risky cash flows. For uncertain payments, the discount rate includes a risk premium. Present value then depends on that assumption.
- Negative rates. If r is negative, the future value is below the present value.
- Day-count conventions. Bond and money markets measure fractions of a year in different ways, so two quotes for the same instrument can differ slightly.
Related terms
Accrued interest · Annualized return · CAGR · Bond duration · Fundamental analysis · Trading glossary
Frequent questions
What is the difference between future value and present value?
Future value moves money forward in time by adding interest. Present value moves money back to today by removing interest.
Why is present value lower than the future amount?
Money held today can earn interest. A later payment is therefore worth less today, as long as the rate is positive.
Which rate should I use for discounting?
Use the rate you could realistically earn over the same period at similar risk. The choice of rate changes the result a lot.
Is this the same as CAGR?
No. CAGR solves for the rate when you already know the start value, the end value and the time. FV and PV solve for a value when you know the rate.