# Time Value of Money: What It Is and How It Works

> **Definition**
>
> The time value of money (TVM), also known as present discounted value (PDV), is a core financial principle that states that money today is worth more than the same amount in the future.

## What Is the Time Value of Money (TVM)?

The time value of money (TVM) suggests that money invested is worth more than its present value. TVM calculates the [future value](https://www.investopedia.com/terms/f/futurevalue.asp) of a sum of money, assuming the cash can grow over time and earn a positive return. 

### Key Takeaways

*   The time value of money doesn't account for losses in capital or negative interest rates.
*   TVM uses the concept of the power of compound interest. 
*   The TVM formula accounts for the amount invested, the rate of return, and the time frame.
*   The formula illustrates the change in money’s value over time, rather than directly computing TVM itself.

![Illustration symbolizing the time value of money with a clock, cash, and coins](https://www.investopedia.com/thmb/kdBWh86uArnD_3uZ_FpNnXDhOak=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/Term-Definitions_Time-value-of-money-1bd784d74c3848d7b2d431569715d0d1.jpg)

*The basic time value of money formula doesn't calculate TVM itself. Instead, it shows the change in the value of money over time. — Investopedia / Mira Norian*

## Power of Compound Interest

A sum of money, once invested, can grow over time. Money deposited into a high-yield savings account will earn interest. Over the ensuing months and years, that interest will be added to the principal, earning more interest. That's what's known as the [power of compound interest](https://www.investopedia.com/terms/c/compoundinterest.asp). 

Money not invested can lose value over time. Hiding $1,000 in a mattress for three years will not only incur a loss of any additional money that could have been earned by investing it, but it will also have even less [buying power](https://www.investopedia.com/terms/p/purchasingpower.asp) than it once did because [inflation](https://www.investopedia.com/articles/investing/090715/how-inflation-affects-your-cash-savings.asp) will have reduced its value.

> **Fast Fact**
>
> The concept of the time value of money is often attributed to Martín de Azpilcueta, a Spanish theologian and economist of the 16th century.

## Time Value of Money Formula

The basic time value of money formula doesn't calculate "TVM" itself. Instead, it shows the change in the value of money over time. It calculates the future value of a sum of money based on:

*   Its present value
*   Interest rate
*   Number of compounding periods per year
*   Number of years

Based on these variables, the TVM formula is:

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

Investors can see the difference between the future value and the present value. The TVM formula may change slightly depending on the situation. For example, in the case of annuity or [perpetuity](https://www.investopedia.com/terms/p/perpetuity.asp) payments, the generalized formula will have additional or fewer factors.

> **Important**
>
> The time value of money doesn't account for any capital losses that may occur or any negative interest rates that may apply.

## Example

Assume a sum of $10,000 is invested for one year at 10% interest compounded annually. The future value of that money is:

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

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:

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

## Effects of Compounding Periods on FV

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: $FV = \$10,000 \times \Big ( 1 + \frac { 10\% }{ 4 } \Big ) ^ {4 \times 1} = \$11,038$
*   Monthly Compounding: $FV = \$10,000 \times \Big ( 1 + \frac { 10\% }{ 12 } \Big ) ^ {12 \times 1} = \$11,047$
*   Daily Compounding: $FV = \$10,000 \times \Big ( 1 + \frac { 10\% }{ 365 } \Big ) ^ {365 \times 1} = \$11,052$

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

## Explain Time Value of Money Like I'm 5

If someone offers you $100 today or $100 a year from now, the $100 today is worth more.

That’s because you can put it to work immediately—by investing it, saving it, or depositing it into a bank account to earn interest. Even at just 1% interest, you’d end up with more than $100 a year from now.

In addition to losing earning potential by not taking the $100 today, you'd also lose out on buying power because of inflation. The costs of goods and services rise over time, and $100 in one year won't buy as much as it would today. 

## How Does the Time Value of Money Relate to Opportunity Cost?

[Opportunity cost](https://www.investopedia.com/terms/o/opportunitycost.asp) is key to the concept of the time value of money. Money can grow only if invested over time and earns a positive return. Money that is not invested loses value over time due to inflation. Therefore, a sum of money expected to be paid in the future, no matter how confidently its payment is expected, is losing value. There is an opportunity cost to payment in the future rather than in the present.

## Why Is the Time Value of Money Important?

The concept of the time value of money can help guide investment decisions. Suppose a business can choose between Project A and Project B. They are identical except that Project A promises a $1 million cash payout in year one, whereas Project B offers a $1 million cash payout in year five. The payouts are not equal. The $1 million payout received after one year has a higher [present value](https://www.investopedia.com/terms/p/presentvalue.asp) than the $1 million payout after five years.

## How Is the Time Value of Money Used in Finance?

The time value of money is the central concept in [discounted cash flow (DCF)](https://www.investopedia.com/terms/d/dcf.asp) analysis, one of the most popular and influential methods for valuing investment opportunities. It is also an integral part of financial planning and risk management activities. Pension fund managers consider the time value of money to ensure that their account holders will receive adequate funds in retirement.

## The Bottom Line

Money's value changes over time. A dollar today is worth more than a dollar tomorrow because of its earning potential. Both individuals and businesses can use the time value of money (TVM) to make smarter investment, spending, and saving decisions.  

> **Article Sources**
>
> 1.  WorldAtlas. "[What Is the Time Value of Money?](https://www.worldatlas.com/articles/what-is-the-time-value-of-money.html)"