# Present Value

You are promised \$P in t periods in the future. The present value, given an interest rate r, is the amount needed to reach P after t periods: $$P = PV \left(1 + r \right)^{t}$$ Therefore, $$PV = \frac{P}{\left( 1 + r \right)^{t}}$$ ## Example You won the lottery and been promised \$100000 in 10 years. You want to know how much money it 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)^{10} &= 100000 \\ PV &= \frac{100000}{\left( 1 + 0.05 \right)^{10}} \\ PV &\approx 61391.32 \end{align*}

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