Week 6 Formulas for TVM

Week 6: Lecture

Formulas for TVM

Study the diagram that we discussed previously carefully (see below).

Notice that there are only four variables (PV, FV, i, and n), and the value of each one depends on the values of the others. This means that given any three of the variables you could solve for the fourth one. You would do this using a set of formulas found below:

Future Value
Remember, we call the $105 you get a year from now the Future Value (FV) of $100 today, after one year has passed, given a rate of return of 5% annually. So, to solve for Future Value (FV):

FV = PV (1+i)ⁿ

Present Value
Remember, we call the $100 you have today the Present Value (PV) of the $105 you expect to receive a year from now, given a rate of return of 5% annually. So, to solve for Present Value (PV):

$PV=FV\left(\frac{1}{\left(1+i\right)^n}\right)$ $PV=FV\left(\frac{1}{\left(1+i\right)^n}\right)$

Rate of Return
Remember, We call the 5% interest rate the rate of return (r or i). The rate is usually symbolized in formulas as r, but you sometimes see it as i, or even k. So, to solve for the rate of return:

Important Note: You should recognize that a rate of return is the same thing as a growth rate. Therefore, the rate of return equation above is equally useful for determining compound growth rates:

This equation can be used to determine the rate of growth per period necessary to reach any ending value (FV) from any starting value (PV) in any given number of periods (n). It is, therefore, a very handy equation i.e., burn it into your memory forever!