# Time Value Of Money: Explained

The time value of money (TVM) is a financial concept that holds that an amount of money is worth more in the present than the same amount of money at a future date. The reason for this is the opportunity cost of receiving money at a date in the future, as opposed to today. Money available today could be invested immediately in a business, an education, or an investment portfolio. Time value of money is a key concept for everyone, not just investors.

## What is the Time Value of Money?

The time value of money concept expresses why it’s more valuable to have $20,000 today than $20,000 in the future. If someone receives $20,000 today, they can invest it immediately. If that same amount is received 10 years from now, the 10 years of waiting represents an opportunity cost.

Since some investments like savings accounts, annuities, dividends, or certificates of deposit provide investors with regular, guaranteed interest that compounds on daily, weekly, monthly, or annual time scales, time has a direct and easily calculated impact on the value of money. Since some monetary growth can be realized essentially free of risk, money is generally worth more when it's received sooner than later.

Inflation, which is usually positive, can be used to express how Time Value of Money exists. Several decades ago, a gallon of milk may have cost $1. Said in reverse, $1 was worth the price of a gallon of milk at that time. Nowadays $1 is worth much less than a gallon of milk. Hence, money held several decades ago was worth more (it bought more) than it does now.

The time value of money is useful because it helps investors make choices about what to do with their money by helping them quantify how much their current assets will be worth over time if invested in different kinds of investment vehicles. Because money invested now can be grown to be worth more in the future, the TVM concept is often used to encourage people to save earlier for retirement. The value of money over time is also often spoken about using terms like time preference or long-term orientation. TVM can be used to calculate the future value of personal or corporate funds and is used in actuarial science and economic theory. It is also a key part of a discounted cash flow analysis (DCF) which is a popular way to determine the future value of invested money.

## How Time Value of Money Works

Consider if someone puts $10,000 into a savings account. If the deposit pays interest at a rate of return of 1% per year compounding annually, the account will have $10,100 at the end of one year. Therefore, on the basis of this example, receiving $10,000 today is essentially equivalent to receiving $10,100 one year from now, and clearly superior to receiving $10,000 one year from now.

### Compounding

When the growth portion of an investment itself begins to increase in value over time, this is called compounding. For investment vehicles without time-specified compounding, time also has an impact since things like securities historically increase in value over time.

## Time Value of Money Formula

While there are online calculators that determine the time value of money, TVM can also be calculated via the time value of money equation. There are many variations of the TVM formula that calculate TVM for different kinds of investment vehicles, however, there are some common formulas used.

Here are the main variables in the time value of money formula:

**Present value (PV):** How much it is currently worth

**Future value (FV):** How much it will be worth in the future

**Number of compounding periods (n):** Whether measured daily, weekly, monthly, quarterly, or annually, the total number of compounding periods over time

**Interest rate (i):** The rate at which your money is expected to grow in the form of a percentage

The simple TVM formula used to calculate the future value of money is:

FV = PV x (1+i)^{n}

One can also calculate the present value of a future sum:

PV = FV/(1 + i)^{n}

There are also variations on the time value of money formulate that helps calculate the value of specific kinds of investments such as annuities.

## Time Value of Money Examples

The best way to understand TMV is with a time value of money example that shows how much investment growth is capable over time with compound interest. If $100,000 is invested in an account, bond, or annuity that compounds annually with a rate of return of 5%:

- There will be $105,000 after one year
- There will be $115,762.50 after three years
- There will be $127,628.19 after five years
- There will be $162,889.46 after 10 years
- There will be $265,329.77 after 20 years
- There will be $432,194.24 after 30 years

Takeaway: The longer money is invested, the faster it grows due to compound interest.

## Present to Future Value

To calculate the future value of money based on the present value, simply plug the investment metrics into the time value of money formula.

- First, identify which numbers correspond with which variables. In this example, $10,000 is being invested for two years at an annual rate of return rate of return of 5%

**Present value (PV):** $10,000

**Future value (FV):** This is what this formula will determine

**Number of compounding periods (n):** 2

**Interest rate:** 5% or 0.05

2. Include the numbers in the formula: FV = PV x (1+i)^{n}

FV = $10,000 (1 + 0.05)^{2}

3. Add up the numbers in the bracket first.

FV = $10,000 (1.05)^{2}

4. Next, raise the number in the bracket to the amount of the exponent.

FV = $10,000 (1.10250)

5. Finally, multiply the present value by the number in the bracket.

FV = $11,025

## Future Value to Present Value

To calculate the present value of money based on the future value, you simply plug the numbers into the formula.

- First, identify which numbers correspond with which variables. In this example, you have $11,025 after an investment of two years at an annual rate of return rate of 5%

**Present value (PV):** This is what this formula will determine

**Future value (FV):** $11,025

**Number of compounding periods (n):** 2

**Interest rate:** 5% or 0.05

2. Include the numbers in the formula: FV = PV x (1+i)^{n}

$11,025 = PV (1 + 0.05)^{2}

3. Add up the numbers in the bracket first.

$11,025 = PV (1.05)^{2}

4. Next, raise the number in the bracket to the amount of the exponent.

$11,025 = PV (1.10250)

5. Finally, divide the future value (FV) by the number in the bracket.

$10,000 = PV

Tip: Using a time value of money calculator will help determine the TVM of an investment quickly.

## Bottom Line

The time value of money is a crucial concept for understanding the impact of time on the value of money, predicting how much individuals and companies need to invest to meet future goals, and calculating the future value of investments. Quantifying the time value of money via a TVM calculation is crucial for financial planning.

This article was written by

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