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Chapter 5
The Time Value of Money
Before You Go On Questions and Answers
Section 5.1
1. Why is a dollar today worth more than a dollar one year from now?
A dollar is worth more today than one year from now, due to its potential earning
capacity. If you have the money in your hand today, you have the opportunity to invest it
and earn interest or you can purchase goods and services for your immediate
con

Transcript

1
Chapter 5 The Time Value of Money
Before You Go On Questions and Answers
Section 5.1
1.
Why is a dollar today worth more than a dollar one year from now? A dollar is worth more today than one year from now, due to its potential earning capacity. If you have the money in your hand today, you have the opportunity to invest it and earn interest or you can purchase goods and services for your immediate consumption. Given that people have a positive preference for consumption, time value of money holds true. 2.
What is a time line, and why is it important in financial analysis? A time line is a horizontal line that starts at time zero (today) and shows cash flows as they occur over time. It is an important tool used to analyze cash flows over certain time periods, as timing of each cash flow has a big impact on the final figure, and therefore on the resulting investment decision.
Section 5.2
1. What is compounding, and how does it affect the future value of an investment? Compounding is the process that refers to converting the initial (principal) amount into a future value. In order to obtain the future value of the principal amount, you calculate what the value at the end of the time period will be assuming the initial investment will earn interest, which is reinvested and will earn additional interest in the future periods.
2 2.
What is the difference between simple interest and compound interest? The difference is the interest earned on interest. 3.
How does changing the compounding period affect the amount of interest earned on an investment? The more frequent the compounding schedule, the higher the interest earned. For example, $100 invested for one year at 10 percent compounded annually will earn you $10 of interest at the end of the year, but if your bank compounded interest quarterly, your earnings from interest would increase to $10.38.
Section 5.3
1. What is the present value and when is it used? Present value is the amount a future sum is worth today given a certain return rate. The present value concept should be used when calculating how much money you need today in order to reach your financial goal sometime in the future. 2
.
What is the discount rate? How does the discount rate differ from the interest rate in the future value equation? The discount rate is the compound interest rate used to determine the present value of future cash flows. Both discount and interest rates essentially represent the same concept. The only difference is the context in which they are used. 3. What is the relation between the present value factor and the future value factor? The present value factor is the reverse of the future value factor. To obtain the present value factor, you divide 1 by the future value factor (1 +
i
).
3 4. Explain why you would expect the discount factor to become smaller the longer the time to payment. The discount factor will become smaller the longer the time to payment due to time value of money. The longer you have to wait to obtain the money, the less value it will have to you. Mathematically, the discount factor is calculated as 1/(1 +
i
)
n
. The longer the time to payment, the larger
n
gets, which will make the discount factor smaller.
Section 5.4
1.
What is the difference between the interest rate (
i
) and the growth rate (
g
) in the future value equation? The interest rate and the growth rate in the future value equation essentially represent the same concept. The growth rate is used when we deal with numerical values such as sales or change over time. When referring to money being invested, we use the term
interest rate.
Self Study Problems
5.1
Amit Patel is planning to invest $10,000 in a bank certificate of deposit (CD) for five
years. The CD will pay interest of 9 percent. What is the future value of Amit’s
investment?
Solution:
Present value of the investment = PV = $10,000 Interest rate =
i
= 9% Number of years =
n
= 5.
4 0 1 2 3 4 5
├───┼───┼───┼────┼───┤
-$10,000 FV
5
=?
5.2
Megan Gaumer expects to need $50,000 as a down payment on a house in six years. How much does she need to invest today in an account paying 7.25 percent?
Solution:
Amount Megan will need in six years = FV
6
= $50,000 Number of years =
n
= 6 Interest rate on investment =
i
= 7.25% Amount needed to be invested now = PV = ? 0 1 2 3 4 5 6 Year
├───┼───┼───┼────┼───┼───┤
PV = ? FV
6
= $50,000
$32,853.85
6
)0725.01(
000,50$
)1(FVPV
nn
i
5.3
Kelly Martin has $10,000 that she can deposit into a savings account for five years. Bank A pays compounds interest annually, Bank B twice a year, and Bank C quarterly. Each
n55
FV PV(1 )FV $10,000(1 0.09)
n
i
$15,386.24

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