How To Calculate Time Value of Money

The cost of using money can be considered from two standpoints. First, money borrowed involves explicit costs in the form of interest demanded by the lender.
Second, all money owned has an implicit cost known as opportunity cost. Opportunity cost is measured by the amount of income that has been foregone. For instance, the opportunity cost of holding idle cash is forgoing the interest that would have been gained.


The time value of money involves the net value of cash flows at different points in time.
Standard calculations based on the time value of money are:
Present value:
The current worth of a future sum of money or stream of cash flows, given a specified rate of return.

Future value:
The value of cash at a specified date in the future is based on the value of that asset in the present.
For any of the equations below, the formula may also be rearranged to determine one of the other unknowns. Bonds can be readily priced using these equations. A typical coupon bond is composed of two types of payments: a stream of coupon payments similar to an annuity, and a lump-sum return of capital at the end of the bond's maturity—that is, a future payment. The two formulas can be combined to determine the present value of the bond.

The interest rate i is the interest rate for the relevant period. The rate of return in the calculations is a predefined variable that measures a discount rate, interest, inflation, cost of equity, and cost of debt. The choice of the appropriate rate is critical to the exercise, and the use of an incorrect discount rate will make the results meaningless.

Formula

PV  -  Present Value
FV  -  Future Value
n    -  number of periods (not necessarily an integer)
I     -  the interest rate at which the amount compounds each period

Future value

The future value (FV) formula is similar

Present value

The present value formula is the core formula for the time value of money; each of the other formulae is derived from this formula.


The present value (PV) formula:

References 

[1] <wikipedia>, '<time value of money>' (online, <2022>) <https://en.wikipedia.org/wiki/Time_value_of_money>.