What is Time Value of Money(TVM)?

The time value of money (TVM) is the concept that a certain amount of money holds more value in the present than it will at a future date, primarily because of its potential to earn during the interim period. This principle is fundamental to finance, emphasizing that having a sum of money in hand is more valuable than having the same sum to be paid in the future. Additionally, the time value of money is commonly known as the present discounted value.

Time Value of Money Formula:

The most fundamental formula for the time value of money has five variables: the future value of money, the present value of money, the interest rate, the number of compounding periods per year, and the number of years. The formula for TVM is:

Where:
FV = Future Value of Money
PV = Present Value of Money
i = Interest Rate
n = Number of compounding periods per year
t = Number of years

This equation can be rearranged to find any unknown variable. For instance, if any four variables are known, we can calculate the fifth variable, which is unknown.

Example of Time Value of Money

Let’s assume a sum of $15,000 is invested for two years at 8% interested compounded annually. The future value of that money is:

This equation can be rearranged to find the value of the future sum of money in present-day dollars. For example, the present-day dollar amount compounded annually at 8% interest that would be worth $7,500 two years from today is:

Effects of Compounding Periods on Future Value

The number of compounding periods has a significant effect on the TVM calculations. Taking the $15,000 example above, if the number of compounding periods is increased to semi-annually, quarterly, monthly, or daily, the ending future value calculations are: