### Unit 4: Time Value Of Money

Suppose you have the option of receiving $100 today or $200 in five years. Which option would you choose? How would you determine which is the better deal? Some of us would rather have less money today vs. wait for more money tomorrow. However, sometimes it pays to wait. Unit 4 introduces the concept of the time value of money and explains how to determine the value of money today versus tomorrow by using finance tools to assess present and future values.

**Completing this unit should take you approximately 7 hours.**

Upon successful completion of this unit, you will be able to:

- explain the time value of money;
- compute present values and future values;
- compute rates of return and know their use in making financial decisions;
- explain when to apply a simple interest calculation versus a compound interest; and
- calculate present values, future values, and payments using non-annual compounding.

### 4.1: The Time Value of Money

This video discusses the difference between present value and future value. The time value of money assumes that individuals face either an increase in prices in the economy as time passes in the form of an inflation rate, such as a 4% annual inflation rate, or an opportunity to put their savings in an investment account offering an interest rate, such as 5% per year. Therefore, under the "time value of money" concept, you can see that the $1,000 that you can receive in two years from today does not have the same value as $1,000 today. In fact, it will have a lesser value today. Likewise, if you receive $1,000 today and have the opportunity to put this money in an investment account earning 5% per year, in two years, you will have more than $1,000.

This video discusses how interest rates are applied. Note that a rate of return is usually expressed as a percentage (such as 4%), but when you need to apply it in a calculation, use it in decimal form (0.04 is the decimal form of 4%, and 0.10 is the decimal form of 10%). The same applies to the numerical expressions of interest rates.

This video discusses how interest rates are applied. When you need to calculate the future value of an amount using a simple interest rate, you apply the interest rate only to the initial amount. On the contrary, when you calculate the future value of an amount using the compound interest rate, you apply the interest rate not only to the initial amount but also to amounts of interest earned. Compounding means you earn interest on interest. It is compounding that allows your savings to grow so much over time.

Read this section that discusses the time value of money. "Why is the time value of money important?". The answer to this question lies in the concepts presented in this section. In finance, a dollar is more valuable today than it is one year or ten years from now. To explain why this is the case, we will give formulas and examples to demonstrate how money is used. As part of this discussion, we will also address why a dollar is worth more today than in the future. Pay particular attention to the definitions and problems presented related to interest rate, future value, and present value.

### 4.2: Future Value and Compounding

Read this section that discusses four separate but related concepts. They include: (1) multi-period investment, (2) approaches to calculating future value, and (3) single-period investment. How are these topics used in the business world? Applying these concepts is helpful when comparing alternative investments and when scarce capital resources are available. Often in a business setting, limited capital resources are available. Therefore, deciding which investment is best depends on comparing which investments will bring the highest returns to the business.

Read this section. You will learn how to calculate the future value of multiple annuities.

This video gives an easy-to-understand demonstration of the power of compounding and why it is so essential that you start saving early.

### 4.3: Present Value and Discounting

This video discusses the basic use of the Present Value (PV) formula when only one period is considered.

This video applies the PV formula when different cash flows are considered in different periods.

This video discusses how to re-calculate the PV amounts when the interest rate changes.

This section discusses how to calculate the present value of a future single-period payment, the return on a multi-period investment over time, and what real-world costs to the investor comprise an investment’s interest rate. It also addresses what a period is in terms of present value calculations and distinguishes between the formula for present value with simple interest and compound interest.

Read this section to see how to use present value to determine the best financing option and calculate the present value of an investment portfolio that has multiple cash flows.

This section gives more detail on computing present and future values. It shows you how to compute more complex problems involving future and present values when there are multiple compounding periods and when the time duration of those problems are longer or are less than one year.

### 4.4: Special Applications: Perpetuities, Annuities and Yields

After reading this section, you will know how to identify, define, and calculate an annuity's present and future value. An annuity is the structure of a financial instrument that is a finite series of level payments that have a definite end. When you are finished, you will be able to recognize the two types of annuities: an ordinary annuity and an annuity due, and explain how they are different. You will also be able to calculate each of these types of annuities and contrast them to their opposites: perpetuities. Annuities are key to understanding because they mimic the payment structure of a bond's coupon payment. This section is foundational for being able to calculate bond prices.

Read about ordinary annuities in this section. The business executive may ask how annuities are used in the real world of business? Pay close attention to how the present value of an ordinary annuity is calculated. Then, the future value of an ordinary annuity is discussed. This is followed by a discussion about when annuities are due. Examples of how and when annuities are used include investments and retirement planning for a regular future payment.

This section discusses calculating perpetuities, a special type of annuity where the stream of payments never ends.

This lesson shows you how to determine the yield (or return) on an investment. It also describes the differences between the effective annual rate and the annual percentage rate.

This section discusses calculating the yield of an annuity, which is the total return received stated as a percent. There are two major methods used to calculate the yield.

This section discusses how to value a series of cash flows and offers a few exercises related to mortgage loans that illustrate how annuities pertain to everyday situations.

### Unit 4 Practice and Assessment

These videos will help you learn to use Excel to solve the Practice and Assessment, rather than purchasing a financial calculator or using the formulas. You may also use calculating apps on your phone. Try practicing doing the homework problems with Excel.

Complete these exercises and problems and then check your work.