Time Value of Money Explained with Formula and Examples (2024)

What Is the Time Value of Money (TVM)?

The time value of money (TVM) is the concept that a sum of money is worth more now than the same sum will be at a future date due to its earnings potential in the interim. The time value of money is a core principle of finance. A sum of money in the hand has greater value than the same sum to be paid in the future. The time value of money is also referred to as the present discounted value.

Understanding the Time Value of Money (TVM)

Investors prefer to receive money today rather than the same amount of money in the future because a sum of money, once invested, grows over time. For example, money deposited into a savings account earns interest. Over time, the interest is added to the principal, earning more interest. That's the power of compounding interest.

If it is not invested, the value of the money erodes over time. If you hide $1,000 in a mattress for three years, you will lose the additional money it could have earned over that time if invested. It will have even less buying power when you retrieve it because inflation reduces its value.

As another example, say you have the optionof receiving $10,000 now or $10,000 two years from now. Despite the equal face value, $10,000 today has more value and utility than it will two years from now due to the opportunity costs associated with the delay.In other words, a delayed payment is a missed opportunity.

The time value of money has a negative relationship with inflation. Remember that inflation is an increase in the prices of goods and services. As such, the value of a single dollar goes down when prices rise, which means you can't purchase as much as you were able to in the past.

Time Value of Money Formula

The most fundamental formula for the time value of money takes into account the following: 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.

Based on these variables, the formula for TVM is:

$\begin{aligned}&FV = PV \Big ( 1 + \frac {i}{n} \Big ) ^ {n \times t} \\&\textbf{where:} \\&FV = \text{Future value of money} \\&PV = \text{Present value of money} \\&i = \text{Interest rate} \\&n = \text{Number of compounding periods per year} \\&t = \text{Number of years}\end{aligned}$​FV=PV(1+ni​)n×twhere:FV=FuturevalueofmoneyPV=Presentvalueofmoneyi=Interestraten=Numberofcompoundingperiodsperyeart=Numberofyears​

Keep in mind, though that the TVM formula may change slightly depending on the situation. For example, in the case of annuity or perpetuity payments, the generalized formula has additional or fewer factors.

Examples of Time Value of Money

Here's a hypothetical example to show how the time value of money works. Let's assume a sum of $10,000 is invested for one year at 10% interest compounded annually. The future value of that money is:

$\begin{aligned}FV &= \$10,000 \times \Big ( 1 + \frac{10\%}{1} \Big ) ^ {1 \times 1} \\ &= \$11,000 \\\end{aligned}$FV​=$10,000×(1+110%​)1×1=$11,000​

The formula can also be rearranged to find the value of the future sum in present-day dollars. For example, the present-day dollar amount compounded annually at 7% interest that would be worth $5,000 one year from today is:

$\begin{aligned}PV &= \Big [ \frac{ \$5,000 }{ \big (1 + \frac {7\%}{1} \big ) } \Big ] ^ {1 \times 1} \\&= \$4,673 \\\end{aligned}$PV​=[(1+17%​)$5,000​]1×1=$4,673​

Effect of Compounding Periods on Future Value

The number of compounding periods has a dramatic effect on the TVM calculations. Taking the $10,000 example above, if the number of compounding periods is increased to quarterly, monthly, or daily, the ending future value calculations are:

• Quarterly Compounding: $FV = \$10,000 \times \Big ( 1 + \frac { 10\% }{ 4 } \Big ) ^ {4 \times 1} = \$11,038$FV=$10,000×(1+410%​)4×1=$11,038
• Monthly Compounding: $FV = \$10,000 \times \Big ( 1 + \frac { 10\% }{ 12 } \Big ) ^ {12 \times 1} = \$11,047$FV=$10,000×(1+1210%​)12×1=$11,047
• Daily Compounding: $FV = \$10,000 \times \Big ( 1 + \frac { 10\% }{ 365 } \Big ) ^ {365 \times 1} = \$11,052$FV=$10,000×(1+36510%​)365×1=$11,052

This shows that the TVM depends not only on the interest rate and time horizon but also onhow many times the compounding calculations are computed each year.

The Bottom Line

The future value of money isn't the same as present-day dollars. And the same is true about money from the past. This phenomenon is known as the time value of money. Businesses can use it to gauge the potential for future projects. And as an investor, you can use it to pinpoint investment opportunities. Put simply, knowing what TVM is and how to calculate it can help you make sound decisions about how you spend, save, and invest.