### Unit 2: Time Value of Money – Future Value, Present Value, and Interest Rates

Suppose you have the option of receiving $100 dollars today vs. $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 2 introduces the concept of time value of money and explains how to determine the value of money today vs. tomorrow by using finance tools to determine present and future values. Also, Unit 2 exposes the concept of interest rates and how to apply them when multiple periods are considered.

**Completing this unit should take you approximately 8 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 the future value and present value of an amount using one period and multiple periods.

### 2.1: The Time Value of Money

This video discusses the difference between present value and future value. The concept called 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 $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. A rate of return is usually expressed as a percentage (like 4%) but when you need to apply it in a calculation, use it in decimal-form (0.04 is the decimal-form of 4%, 0.10 is the decimal-form of 10%, and so on). 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. The compound interest rate is commonly used by banks, credit card companies, and any other financial institution. The simple interest rate is usually applied to loans made in informal business deals, and even to loans involving family members!

- 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 the finance world, a dollar is more valuable today than it is 1 year or 10 years from now. To explain why this is the case, formulas and examples are presented that demonstrate how money is used. As part of this discussion, we'll talk about why a dollar is worth more today than in the future. Pay particular attention to the definitions and problems presented that relate to interest rate, future value, and present value.
- 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 in duration.
- 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.

### 2.2: 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? The application of these concepts is useful when comparing alternative investments and scarce capital resources are available. Often in a business setting, limited capital resources are available. Therefore, the decision concerning which investment is best depends on comparing which investments will bring the highest returns to the business.

Read this section that discusses Future Value and Multiple Flows. You will learn how to calculate the future value of multiple annuities.

Read about ordinary annuities in this article. 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, retirement planning for a future regular payment.

### 2.3: 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 recalculate the PV amounts when the interest rate changes.

### 2.3.1: Present Value, Single Amount

- Read this section that discusses how to calculate the present value of a future, single-period payment; the return on a multi-period investment over time; what real-world costs to the investor comprise an investment's interest rate; what a period is in terms of present value calculations; and how to distinguish between the formula used for calculating present value with simple interest and the formula used for present value with compound interest.

### 2.3.2: Present Value, Multiple Flows

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.

### 2.3.3: How Capital Budgeting is Used to Make Decisions

Read this section about capital budgeting, decision-making, net present values, annuity tables, and internal rate of return. This section gives examples of how large corporations use capital budgeting techniques when they invest in real estate projects or large equipment projects.

### 2.3.4: Present Value Interest Factor

Read this section that presents four scenarios that each pertain to the time value of money. First, the time period to reach a single amount target sum. Second, the time period to reach an annuities maturity. Third, the growth rate of a single amount. And fourth, the growth rate of an annuity. The application of these topics can be helpful on an individual level when considering investments and comparing which investments are going to give the highest projected return.

### 2.4: Variable Rates of Return

This video shows you how to use the future value formula when you are considering an interest rate that applies every six months but it is quoted on an annual basis.

This video shows how to use the future value formula when you are considering the annual interest rate on a daily basis.

This video reviews what you learned from the first two videos.

This video demonstrates what it means to use an annual interest rate continuously.

### 2.4.1: Time-Varying Rates of Return and the Yield Curve

Read this section about the time-varying rates of return and the yield curve, and bonds and the yield curve. Sensitivity to changes in interest rates are also discussed. It also applies these concepts to show how a manager or executive can use them. There is some class-specific information from the professor who created this document; you can ignore it.

### 2.4.2: Time Varying Interest Rates and Yield Curves

This section explains five topics that are important to businesses: (1) The fixed income market, (2) The varying interest rates and yield curves, (3) A model for stochastic interest rates, (4) The risk of rolling over, and (5) Implications of the yield curve. Why are these topics important to the business owner or executive? These topics are used when the returns on investments are sought by investors. There is some class-specific information from the professor who created this document; you can ignore it.

### 2.5: Special Applications: Perpetuities and Annuities

- After reading this section, you will know how to identify, define, and calculate the present and future value of an annuity. An annuity is the name for 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. Also, you will be able to calculate each of these types of annuities, and contrast them to their opposite, a perpetuity. Annuities are key to understand because their structure mimics the payment structure of a bond's coupon payment. This section is foundational for being able to calculate bond prices.
- This section discusses calculating perpetuities, which are a special type of annuity where the stream of payments never ends.
- 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 annuities and offers some exercises relating to mortgage loans that illustrate how annuities pertain to everyday situations.

### Unit 2 Assessment

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Take this assessment to see how well you understood this unit.

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**does not count towards your grade**. It is just for practice! - You will see the correct answers when you submit your answers. Use this to help you study for the final exam!
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