# Time Value of Money Formula Sheet

**Symbols:**

**PV = Present value, what future cash flows are worth today**

**FV = Future value, what cash flows are worth in the future**

**r = interest rate, rate of return, or discount rate per period – typically, but not always, one year**

**n = number of periods – typically, but not always, the number of years**

**C = cash amount**

**Basic Time Value Calculations**

- How much will I receive in the future if I investment certain amount today? (compounding)
- FV = PV(1 + r)
^{n}

- FV = PV(1 + r)
- How much do I have to invest today to have some amount in the future? (discounting)
- PV = FV / (1 + r)
^{n}

- PV = FV / (1 + r)
- What is the implied interest rate in an investment?
- r= (FV / PV)
^{1/n}– 1, or

- r= (FV / PV)
- How to find the number of time periods?

**Annuity and Perpetuity Calculations**

- Present value and future value of ordinary annuity

- Present value of a Perpetuity: PV=C/r