Time Value of Money

Future value, present value, compounding, and discounting formulas.

Future Value (Compound Interest)

PV = present value, r = interest rate per period, n = number of periods.

FV = PV \cdot (1 + r)^n

Present Value (Discounting)

How much a future cash flow is worth today.

PV = \frac{FV}{(1 + r)^n}

Compound Interest (Multiple Compounding Periods)

m = number of compounding periods per year.

FV = PV \cdot \left(1 + \frac{r}{m}\right)^{m \cdot n}

Net Present Value (NPV)

Sum of discounted cash flows minus initial investment. CF_t = cash flow at time t, r = discount rate.

NPV = \sum_{t=0}^{n} \frac{CF_t}{(1 + r)^t}

Perpetuity

Present value of an infinite stream of constant payments C at discount rate r.

PV = \frac{C}{r}

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