Time Value of Money

Course Introduction

Course Introduction

Think about this...

  • How will being informed with my personal values relate to my needs and wants?
  • Will needs and wants change from individual to individual, family to family? Why or why not?
  • How can setting financial SMART goals help you better reach a financial objective?
  • Why should I invest? 

Financial Planning 

Your financial goals are specific objectives that are accomplished through financial planning. Financial planning involves managing money continuously through life in order to reach your financial goals. Your financial plan will continually change as your life changes.  Setting financial goals and financial planning is an ongoing process that should be considered and evaluated throughout your entire life.

Time Value of Candy

Time Value of Candy

Imagine This...

All right, let's do a little thought experiment. 

Imagine you are a three-year-old child.  

Do you have the visual? 

Now imagine I offer you one piece of chocolate now OR one piece of chocolate tomorrow

Which would you take? 

It's a safe bet that you're probably going to take the chocolate now.  

Any child understands what we will call the "time value of candy". Candy NOW is worth more than candy in the future.   


But what if I offer you one piece of chocolate now OR five pieces tomorrow?  

A three year old would still probably take the one piece now. For a young child, the future is such an unpredictable and vague place that it makes sense to take your candy now. In fact, an important part of growing up is learning that planning an action now have predictable consequences for the future. 

Let's change the example...

Imagine you are you. 

I offer you 100 pieces of chocolate now or you can go without chocolate for an entire year and I give you 100 pieces of chocolate one year from now.  You'll probably take the 100 pieces of chocolate now.

How about I offer you 100 pieces now -- OR --  200 pieces one year from now? 

Now it's safe to say you're probably going to wait and take the 200 pieces one year from now. 

You see that people prefer candy (or money) now to candy (or money) in the future. But there is some extra amount in the future, some amount of interest, that can cause you to wait. 

In this last example, your chocolate interest rate was 100%. I had to agree to double your chocolate to get you to wait one year. 

Needs, Wants, and Values

Time Value of Money

It's important to be able to estimate the value of an investment in the present and in the future.

The idea that money available at the present time is worth more than the same amount in the future due to its potential earning capacity is called the time value of money. 

This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received. Thus, at the most basic level, the time value of money demonstrates that, all things being equal, it is better to have money now rather than later.

But why is this? A $100 bill now has the same value as a $100 bill one year from now, doesn't it? Actually, although the bill is the same, you can do much more with the money if you have it now because over time you can earn more interest on your money.

By receiving $10,000 today (Option A), you are poised to increase the future value of your money by investing and gaining interest over a period of time. If you receive the money three years down the line (Option B), you don't have time on your side, and the payment received in three years would be your future value. To illustrate, we have provided a timeline:

Option A

If you choose Option A, your future value will be $10,000 plus any interest acquired over the three years. 

Option B

The future value for Option B, on the other hand, would only be $10,000. So how can you calculate exactly how much more Option A is worth compared to Option B? 

Let's take a look.

Future Value Basics

If you choose Option A and invest the total amount at a simple annual rate of 4.5%, the future value of your investment at the end of the first year is $10,450, which is calculated by multiplying the principal amount of $10,000 by the interest rate of 4.5% and then adding the interest gained to the principal amount:

Future value of investment at end of first year: 
= ($10,000 x 0.045) + $10,000 
= $10,450

You can also calculate the total amount of a one-year investment with a simple manipulation of the above equation:

  • Original equation: ($10,000 x 0.045) + $10,000 = $10,450
  • Manipulation: $10,000 x [(1 x 0.045) + 1] = $10,450
  • Final equation: $10,000 x (0.045 + 1) = $10,450

The manipulated equation above is simply a removal of the like-variable of $10,000 (the principal amount) by dividing the entire original equation by $10,000.

If the $10,450 left in your investment account at the end of the first year is left untouched and you invested it at 4.5% for another year, how much would you have? 

To calculate this, you would take the $10,450 and multiply it again by 1.045 (0.045 +1). 

At the end of two years, you would have $10,920:

Future value of investment at end of second year: 

= $10,450 x (1+0.045)
= $10,920.25

Think back to math class and the rule of exponents, which states that the multiplication of like terms is equivalent to adding their exponents. In the above equation, the two like terms are (1+0.045), and the exponent on each is equal to 1. Therefore, the equation can be represented as the following:

We can see that the exponent is equal to the number of years for which the money is earning interest in an investment. So, the equation for calculating the three-year future value of the investment would look like this:

This calculation means that we don't need to calculate the future value after the first year, then the second year, then the third year, and so on. If you know how many years you would like to hold a present amount of money in an investment, the future value of that amount is calculated by the following equation:

Future Value

= Original Amount x ( 1+ interest rate per period) number of periods
OR 
= P * (1=i)n

SMART Goals

What Does SMART Mean? 

SMART is an acronym that you can use to guide your goal setting.

To make sure your goals are clear and reachable, each one should be:

  • Specific (simple, sensible, significant).
  • Measurable (meaningful, motivating).
  • Achievable (agreed, attainable).
  • Relevant (reasonable, realistic and resourced, results-based).
  • Time bound (time-based, time limited, time/cost limited, timely, time-sensitive).

Step One: Write it Down! 

The first step in setting a SMART goal is to create a specific goal and write it down. Once you know your goal, you will follow the next steps below:

Step Two: Analyze Information

After you set your SMART goal, you need to analyze the information. 

Use the following scenario and SMART goal: 

I will put $400 bi weekly (every payday) into a savings account to save $4,000.00 in order to go on vacation in 5 months. 

Now you just need to analyze:

  • Where does my money go each week?
  • Does the $400 fit into my budget?
  • If not, where can I cut spending?
    - You may need to write a subgoal to meet your larger goal.

Step Three: Create a Plan 

Creating a plan is your financial road map. 

This occurs after you analyze the situation and make the best decision you can. 

We included this step when we created the SMART goal. 

We took the total amount we needed to save and divided it by the number of weeks/paychecks we had to reach our deadline date.

Step Four: Implement the Plan

Making it happen. With your plan in place, the next step is to implement it. 

Of course, knowing what you should do is one thing. Actually doing it can be challenging. It takes discipline.

Step Five: Monitor and Modify the Plan

Staying on track. The best way to do this is decide to review your plan and your progress at regular intervals -- like every two weeks or every month. The more often you do this, the sooner you'll catch yourself if you start straying off course.

If something comes up, you need to be able to modify your plan. Maybe you decided you can put more than the expected amount away per week. Or maybe you decided you need more than expected and thus need to adjust your goal.

SMART Goals and Investing

Getting what you want doesn't always come easily. Chances are you'll have to work to reach your goal. Achieving what you want financially—whether saving to buy a house or for a fun vacation—requires the same planning, perseverance and know-how. 

Compare the two sets of goals below. The general goals simply state what you hope or want without specifics to help you along. The SMART goals provide you with specific and measurable targets to work toward both in terms of a dollar amount and timeframe.

General Goals

  1. Hope to get out of debt
  2. Want to buy a house
  3. Want to send my children to college


SMART Goals

  1. Will be out of debt by January of next year based on monthly payments of $600
  2. Will buy a home in two years with $10,000 saved for a down payment
  3. Will have $18,000 saved for college in 10 years when my child is 18 years old

Short-Term Goals 
(Less Than a Year)

  • Emergency fund
  • Buying a TV
  • Buying new furniture
  • Going on vacation

Mid-Term Goals 
(One to Three Years)

  • Getting out of debt
  • Buying a car
  • Buying a home
  • Emergency fund

Long-Term Goals
(More than Three Years)

  • College fund
  • Retirement
  • Vacation home
  • Emergency fund

Time Value of Money Quiz

The amount of money a person expects to have in the future is called

  • Principal
  • Simple Interest
  • Present Value
  • Future Value

Earning interest on interest is called

  • Extra Interest
  • Inflation Interest
  • Compound Interest
  • Simple Interest

The idea that money to be paid out or received in the future is not equivalent to money paid out or received today

  • Time Value of Money
  • Compound Money
  • PV/FV Money
  • SMART Money

The A in SMART Goals stands for

  • Acceptable
  • Additional
  • Attainable
  • Accurate

A fast way to estimate how long it will take your savings to double with compound interest is known as

  • 70-20-10 Rule
  • Rule of 72
  • Rule of the 70's
  • 30-60 Rule

You invest $475 in an account that pays 3% simple interest annually. How much money do you have after five years?

  • $546.24
  • $546.25
  • $544.46
  • $543.25

You invest $800 in an account that pays 6% interest, compounded annually. How much money do you have after five years? Round your answers to the nearest cent.

  • $898.09
  • $975.68
  • $1070.58
  • $1710.58
  • $1710.01

Sarah invests $7,300 at 6% interest compounded annually for four years. What is the future value of this investment?

  • $9,216.08
  • $6,236.83
  • $6,240.07
  • $9,246.57

Steady rise in the general level of prices is known as

  • Inflation
  • Interest
  • Principal
  • Time Value of Money

Sally invested $6,500 in a savings account earning 12% interest compounded quarterly. What is the future value of this investment after five years? Round your answers to the nearest cent.

  • $1,235,322.65
  • $6,901.32
  • $6,895.85
  • $11,739.72