What is time value of money
Time value of money means that a sum of money available today is worth more than the same sum received later, because money held today can earn interest in the meantime.
Formal definition
The time value of money is the principle that a cash flow's value depends on when it arrives. To compare cash flows at different dates, you move them to a common date with an interest rate, called the discount rate when you move money backwards in time.
- Present value (PV): what a future amount is worth today.
- Future value (FV): what an amount today grows to after a given time.
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Time value of money formula
Each period, the amount is multiplied by a growth factor: the whole amount plus the interest rate for that period. Over n periods with rate r per period:
- FV = PV × (growth factor)^n
- PV = FV ÷ (growth factor)^n
Dividing by the growth factor is called discounting. Multiplying by it is called compounding. To test your own figures, use the tools on the Calculators page.
Worked example (hypothetical)
Interest rates in Pakistan start from the State Bank's policy rate. The latest decision: SBP policy rate raised by 50 bps to 12% with effect from 27.10.2026 (MPC).
Suppose, as a hypothetical case, a bank deposit paid a yearly rate equal to that policy rate:
| Choice | What happens |
|---|---|
| Take Rs X today and deposit it | After a year you have Rs X plus a year of interest |
| Take Rs X in a year | You have only Rs X |
The first choice is worth more. Turned around, the present value of Rs X promised in a year is less than Rs X: you divide it by the growth factor.
Where the term appears
- Bonds: a bond's price is the present value of its coupons and face value. Accrued interest and bond duration are built on it.
- Forex and CFDs: overnight swap fees reflect the interest difference between two currencies. Forward points and covered interest parity follow the same logic. Leveraged CFD and forex trading can lose money fast, and swaps add to the cost of holding a position.
- Loans: amortization schedules split each payment into interest and principal using present value.
- Reports and news: annualized return, CAGR and policy rate changes quoted in basis points are all time value of money ideas.
Edge cases for experienced readers
- Compounding frequency: a yearly rate compounded monthly gives a higher future value than the same rate compounded yearly. Continuous compounding uses FV = PV × e^(rt).
- Nominal vs real: inflation reduces purchasing power. A real rate subtracts inflation. In deflation, cash gains purchasing power even with no interest.
- Negative rates: when rates are below zero, discounting can make a future amount worth more than the same amount today.
- Risk: a risky promise gets a higher discount rate, which is why credit spreads exist and why a default risk lowers present value.
Related terms
Basis point · Coupon · CAGR · Annualized return · Forward contract · Trading glossary · Saving, Investing, Loans
Frequent questions
What is the time value of money in simple words?
Money today is worth more than the same money later, because today's money can earn interest.
What is the difference between present value and future value?
Present value is what a future sum is worth today. Future value is what today's sum grows to. One is the other moved forward or backward in time with an interest rate.
Which rate should I use as the discount rate?
It depends on the case. People often use a deposit rate, a bond yield or the policy rate as a reference, plus extra for risk.
Does inflation change the time value of money?
Yes. Inflation reduces what money buys, so real returns are lower than nominal ones.
Does this give any trading signal?
No. It is a valuation principle, not a forecast or a recommendation.