Time Value of Money: Definition, Formulas, and Examples

Time value of money is a basic concept that can help you make personal financial decisions. When you understand this concept, you can determine the value of your money today compared to the same amount in the future.

Through this concept, you can also determine the value of various investment options based on their interests and when they get them. In this article, we explain the concept of the time value of money and provide an example of how to calculate it.

What is the time value of money?
What is the formula for the time value of money?
Examples of the time value of money

3.1 Example 1
3.2 Example 2
3.3 Example 3
Time value of money and compound interest
Time value of money and opportunity cost

What is the time value of money?

The concept of the time value of monkey (TVM) states that the money you have today is worth more than the same amount in the future. The reason being, your current money has the potential to grow if you invest it or keep it and earn interest, for example. Understanding these concepts can help you make important buying, business, and banking decisions.

The time value of money is also related to the concepts of inflation and purchasing power. Inflation causes prices to increase over time, which means that the money you have today can buy more things now than you can in the future. You can potentially fight inflation by investing money in the stock market, not in savings accounts that offer interest rates below inflation rates.

What is the formula for the time value of money?

The formula for calculating the time value of money changes slightly depending on your situation, but the general equation consists of the following variables:

  • FV = Future value of money
  • PV = Present value of money
  • i = Interest rate per period
  • n = Number of compound interest periods per year
  • t = number of years or the length of time the money is kept

Using these variables, the resulting formula is:

FV = PV x [1 + (i/n)] ^ (nxt)

Similarly, you can rearrange the formula to find the present value of future money:

PV = FV / [1 + (i / n)]^(nxt)

Example of the time value of money

The following example shows how to calculate the time value of money :

Example 1

A relative has offered to give you 8,000,000 and asked if you would rather receive the money today or wait two years. To make sure that getting 8,000,000 today is worth more than if you waited, you can calculate its future value.

If you decide to take 8,000,000 and invest in an account at a 6% annual rate, you will do the following calculations to find out its value in two years:

FV = 8,000,000 x [1 + (6%/1)] ^ (1 x2) or FV = 8,000,000 x (1 + 0.06)^2

In two years, your 8,000,000 investment will be worth 8,988,800. You can see that it is worth more to take 8,000,000 today than waiting two years to receive 8,000,000 because that gives you 988,800 more.

Example 2

You can also find the present value of 8,000,000 that you can receive in two years. Using the same interest rate as before, your calculation should look like:

PV = 8,000,000 x (1+ 0.06) ^ -2

Performing this calculation, you find that the present value of the sum is 7,119,970. This shows you that receiving 8,000,000 in the future works as if you took 7,119,970 today and invested it over two years.

Again, you can see that receiving 8,000,000 today will get you more value than waiting.

Example 3

You receive a cash bonus, but your employer gives you two choices: receive 8,000,000 now or 10,000,000 two years from now. 10,000,000 in two years may seem more attractive at first because it is a higher number.

To determine which option to choose, you need to determine whether investing 8,000,000 today will earn you more money than 10,000,000 in two years. If you invest 8,000,000 into an account that earns 12% annual interest, your equation will be:

FV = 8,000,000 x [1 + (12% / 1)] ^ (1 x 2)

Using this calculation, you find that the future value of your 8,000,000 invested in an account earning 12% annual interest, in two years will be 10,035,200.

Taking money today is better because you have the ability to increase its value to an amount greater than what your boss promised you in two years.

Time value of money and compound interest

While inflation can decrease the future value of your money, compound interest can combat that effect and help increase the current value of your money in the future.

Therefore, it is more valuable to invest your money now than to spend it. Compound interest refers to the amount of interest calculated based on the initial amount of money you invested and the interest accumulated over a certain period.

Compound interest periods can vary, such as daily, monthly, and quarterly. Depending on the compounding period, your account will receive interest on a daily, monthly or quarterly basis.

Here is an example of how different compounding periods affect the future value of money:

Annual compounding period:

$14,000 x [1 + (11% / 1)]^(1 x 1) = $15,540
Quarterly compounding period

$14,000 x [1 + (12% / 4)]^(4 x 1) = $15,604.70
Monthly compounding period:

$14,000 x [1 + (12% / 12)]^(12 x 1) = $15,620.06
Daily compounding period:

$14,000 x [1 + (12% / 365)]^(365 x 1) = $15,627.63
You can see that daily combined accounts will give you a bigger return on investment in less time.

Time value of money and opportunity cost

When making financial decisions based on the time value of money, you should also consider opportunity costs. If you have several options to choose from when making a decision, opportunity cost refers to the potential profit you would not receive because you chose one option over another.

Here is an example of the time value of money and opportunity cost:

You are a business owner and need to decide how to spend $10,000. You can spend it on buying new equipment that will give you a 5% annual return or put it in an investment account that offers an annual return of 8.5% interest. Using the time value of money formula , you can calculate your options:

$10,000 x [1 + (5% / 1) ^ (1 x 1) = $10,500

$10,000 x [1 + (8.5% / 1) ^ (1 x 1) = $10,850

In this scenario, your opportunity cost is $350 which you would have missed buying the equipment instead of investing the money.


That’s a complete discussion about the time value of money that may be useful when you make an investment or decide to buy assets in your business. Calculating the time value of money is important to ensure that the investments you make are running effectively and you will not suffer losses in the future.

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