# Time Value of Money (TVM): Core Concept
## The central idea
The Time Value of Money states that a rupee available today is worth more than a rupee received in the future. This is because money in hand can be invested to earn a return, so the same nominal amount has different real worth depending on when it is received or paid.
TVM lets us:
- Compare cash flows occurring at different points in time on a common footing.
- Make sound decisions about investments, loans, and any situation where money moves across time.
It is a core principle of finance and underlies almost every other FM topic (cost of capital, capital budgeting, valuation).
## The two TVM techniques
There are two complementary techniques. Both rely on the same interest rate `r₹ and number of periods `n`.
| Technique | Direction | Meaning | Formula |
|---|---|---|---|
| Future Value (Compounding) | Today → Future | The cash value of an investment at some future date — tomorrow's value of today's money compounded at the rate of interest. | `FV = PV (1 + r)ⁿ₹ |
| Present Value (Discounting) | Future → Today | Today's value of tomorrow's money — future money discounted at the interest rate. | `PV = FV / (1 + r)ⁿ₹ |
### How to read the formulas
- Compounding grows a present amount forward: multiply by ₹(1 + r)ⁿ`.
- Discounting shrinks a future amount back: divide by ₹(1 + r)ⁿ`.
They are mirror images: discounting simply reverses compounding.
## Notation recap
- `PV₹ = Present value (value today)
- `FV₹ = Future value (value at end of `n₹ periods)
- `r₹ = interest / discount rate per period
- `n₹ = number of periods