# Time Value of Money Examples

Imagine your company gives you an option: receive a one-time bonus of \$500 today or the same amount of money in two weeks. You’re probably going to take the money immediately. But why?

First and foremost, money is scarce and it’s better to have any sum of money as quickly as you can. Otherwise, you’re opening the door to a variety of risks that could threaten your ability to receive the payment.

In addition, you must consider the time value of money — one of the core elements of finance, and one of the most important foundational concepts you can learn as an investor.

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

In short, the time value of money concept is the fancy way of defining the classic idiom that tells us time is money.

In other words, the time value of money principle states that a dollar today is worth more than its equivalent sum in the future and that the purchasing power of a single dollar decreases over time. Just think about how much a dollar could buy you 100 years ago and how you might not be able to even buy a soda with one today.

This is primarily due to the opportunity for earning capacity. In other words, money can earn interest over time and grow into a larger sum. It’s also due to inflation. Money will be worth less next year because prices tend to increase over time (more on this below).

## Time Value of Money Examples

At this point, you understand the basic concept of the time value of money. But to further your understanding, we will examine some common ways you can apply the time value of money to your everyday finances.

### Future Value of Money

The time value of money formula can determine the future value of money after taking into consideration interest and compounding time periods.

You can use the following equation in a program like Excel to calculate the time value of money where FV equals future value, PV equals present value, i refers to the interest rate, n is the number of compounding periods of annual interest, and t is the number of years you are considering:

• FV = PV x [1 + (i / n) ] (n x t)

For example, suppose you invest \$10,000 for one year, compounded at 10% interest. The formula would be FV = \$10,000 x [1+(10%/1)] ^ (1 x 1) = \$11,000. In other words, your investment would be worth \$11,000 at the end of the year.

Now, try this: Plug in a 5% interest rate, and you’ll end up with \$10,500 at the end of the year. So as you can see, this is a great way to compare different savings plans with varying interest rates.

### Present Value of Future Money

Calculating the present value of money can let you understand what your money will amount to at a future date. Going back to our above example, you may want to determine how much money you would need right now to reach \$11,000 in savings a year down the road. To run this calculation, simply divide the future value instead of multiplying the present value.

With all variables remaining the same in our last example, the formula now becomes:

• PV = \$11,000 / (1 + (10% / 1) ^ (1 x 1) = \$10,000

### Net Present Value (NPV)

Net present value refers to the difference between the present value of cash outflows and the present value of cash outflows over time.

Net present value is commonly used in investing planning to understand the current value of future cash inflows by a project, along with the initial capital investment.

For example, a company may use NPV as part of a capital budgeting calculation to understand which projects will turn the highest profits. Based on that information, they could then figure out which projects to prioritize and pour more resources into.

## Time Value Money: Key Concepts

Now that you have a basic understanding of how the time value of money is applied to everyday financial situations, let’s take a look at some important fundamental concepts to deepen your learning.

### Money is Worth More Today than Tomorrow

Money is worth more today than tomorrow due to two factors: compound interest and inflation, which increases prices over time. As a result, your dollar will buy you more at the present time than it will at a future date.

For this reason, it’s critical to start investing as soon as possible — especially when considering that the stock market is designed to beat inflation.

This is also why it hurts to make or receive payments long after they are due. The payment decreases in value with every day that goes by.

### Opportunity Cost

Another key concept to keep in mind when thinking about time value money is opportunity cost. Essentially, this means that every choice you make comes with a sacrifice.

For example, investing \$10,000 in a certificate of deposit account will give you the opportunity to secure a fixed interest rate for a set period of time. However, the cost will be that you won’t be able to grow the money in the stock market and potentially earn more in interest.

Calculating opportunity costs can come in handy when deciding whether to invest money or pay off debt. For example, you can run an opportunity cost calculation to figure out the cost of putting money into the stock market instead of paying down a credit card with a 25% APR.

### Risk and Return

The principle of risk and return explains that the potential for return increases as you take on more risk.

For example, you should assess risk and return when calculating a long-term investment. By increasing your risk in the form of higher monthly payments, you can improve your potential return over time.

Investing is hard work. If it were easy, everyone would be a millionaire. If you’re unsure about which investment strategies are best for you, consider working with a financial advisor to determine your exact risk tolerance. That way, you will have a clear idea about how much risk you can afford on an annual basis.

## Advantages to Using Time Value of Money Formulas

Now that you have a more holistic understanding of the time value of money, here are some of the top advantages of thinking about this metric.

Let’s face it: Not everyone is great about making payments on time. Sometimes, you have to be assertive and put your foot down to collect what you’re owed.

The time value of money formula is a tool you can use to justify how much a late payment is potentially costing you in interest. You can use this tool as leverage to collect money that is legally yours by charging a rate of interest to the party that owes you money if they don’t pay on time.

### Make Informed Financial Decisions

It’s not always easy to determine what to do with money. For example, should you take a lump sum of cash and pay down your mortgage, put it in the bank so that it can securely grow, or pump it into the stock market to maximize long-term return on investment?

The time value of money formula can help you understand your best option based on a variety of factors, including risk, expected return, annual interest rate, and inflation, among other things. Doing this before making an investment can help you ensure that you are making the right financial moves at the right time.

### Maximize Time

Once you start associating money with time, it fundamentally changes the way you approach money management

By understanding how money loses value over time, you’ll begin to see the damage of letting checks go uncashed for weeks or letting money rot away in checking or savings accounts with low-interest rates.

As they say, time is precious — especially when it comes to finances.

### Why should you start investing in your 20s?

It’s never too late to start investing. But it’s never too early to start investing, either. By starting to invest earlier in life, you can put money into the stock market so that it can beat inflation. Plus, you’ll have decades ahead of you for money to collect compound interest and compound gains.

The longer you wait to invest, the more you will cost yourself in potential interest. And unfortunately, time is something you can’t get back as an investor. As such, it’s important to treat time as one of your most precious assets.

### How do you calculate the present value of an annuity?

An annuity refers to recurring or ongoing payments such as interest from a certificate of deposit (CD) and pension payments. Annuities may also refer to recurring payments that are allocated toward rent or a mortgage.

There are two types of annuities: ordinary annuity and annuity due. The former requires payments at the end of each period while the latter requires payments at the beginning of each period.

#### Calculating Future Value for Ordinary Annuities

Use the following formula to calculate a future value for ordinary annuities:

• P = PMT [((1 + r)^n – 1) / r]

P: future value of annuity stream

PMT: amount of each annuity payment

r: interest rate

n: number of periods for making payments

#### Calculating Future Value for Annuities Due

Here’s how to calculate the future value for annuities due:

• P = (PMT [((1 + r)n – 1) / r])(1 + r)

### What is perpetuity?

A perpetuity is a type of security that pays for an infinite period of time — or a series of infinite cash flows that occur at the end of each period with an equal interval of time between them.

### What is discounting?

Discounting is used to determine the present value of a payment or stream of payments received in the future.

For example, with bonds, coupon payments are discounted by interest rates and added together with a par value to determine its current value.

## The Bottom Line

People who are new to saving and investing tend to make assumptions on blind faith based on numbers that they are given by financial institutions or online experts. However, this is an easy way to get manipulated or ripped off — or make suboptimal decisions at the very least.

Understanding the time value of money helps you approach finances in a whole new light. The better approach is to think about the time value of money and run calculations on future payments to determine their overall value. This is a great way to see how the value of an investment changes over time, which helps you make the best financial decisions right now

One last thing: It’s not like you have to get out your scientific calculator and run all of these equations by hand. If you have trouble running formulas on your own, consider using free online financial calculators to help you make quick and easy valuations. That way, you can quickly crunch the numbers and get the information you need.