# Net Present Value

The Net Present Value (NPV) is the difference between the Present Value (PV) and the Present Cost (PC): $$NPV = PV - C$$

## Example

You gave \$10000 to a friend who promised to give you \$12000 back in 3 years.

You want to know how much money \\$12000 in 3 years corresponds to today if you were to save some money in the bank at a 5% interest rate. The present value (PV) solves \begin{align*} PV \left( 1 + 0.05 \right)^{3} &= 12000 \\ PV &= \frac{12000}{\left( 1 + 0.05 \right)^{3}} \\ PV &\approx 10366.05 \end{align*} The Net Present Value is $$NPV = PV - PC = 10366.05 - 10000 = 366.05$$ That's a pretty good deal.

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