Practice Exam 1
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Exam 1
Practice Exam
1.
What is the relationship between future value and present value?
FV
=
PV
(
1
+
r
)
t
2.
For a given time period and future value – the lower the interest rate, ___________ the present value.
For a given time period and future value – the lower the interest rate, higher
is the present value.
3.
Your best friend from FIN324 invested $3,000 five years ago and earns 2 percent annual interest. By leaving her interest earnings in her account, she increases the amount of interest she earns each year. The way she is handling her interest income is referred to as:
a.
simplifying.
b. compounding.
c.
aggregating.
d. accumulating.
e.
discounting.
Solution: b. compounding
4.
If the monthly interest rate is 1%. What is the annual interest rate?
r
monthly
=
1%
r
annual
=
(
1
+
r
monthly
)
12
−
1
r
annual
=
(
1.01
)
12
−
1
=
12.68%
5.
Calculate the present value of the following cash flows discounted at 10 percent
per year.
a.
$100,000 received 10 years from today.
PV
=
FV
(
1
+
r
)
t
=
100,000
1.1
10
=
$
38,554.33
b.
$100,000 received 2 years from today.
PV
=
¿
100,000
1.1
2
=
$
82,644.63
c.
$100,000 received 20 years from today.
PV
=
¿
100,000
1.1
20
=
$
14,864.36
6.
If you put up $36,000 today in exchange for a 7.00 percent, 18-year annuity, what
will the annual cash flow be?
PV
=
C
r
(
1
−
1
(
1
+
r
)
t
)
36,000
=
C
.07
(
1
−
1
1.07
18
)
C
=
$
3,578.85
7.
You deposit $2,000 at the end of each year into an account paying 10.6 percent
interest.
a.
How much money will you have in the account in 24 years?
FV
=
C
r
[
(
1
+
r
)
t
−
1
]
=
2000
0.106
[
(
1.106
)
24
−
1
]
=
$
192,893.66
b.
How much will you have if you make deposits for 48 years?
FV
=
C
r
[
(
1
+
r
)
t
−
1
]
=
2000
0.106
[
(
1.106
)
48
−
1
]
=
$
2,357,809.41
8.
Shao Professional Basketball Agents issued a 17-year bond 2 years ago at a
coupon rate of 10%. The bond makes semi-annual payments. The bond currently
sells for 102% of par value. If the YTM changes from 9.75% to 12%, where will the
bond be traded?
a) The bond will be traded above par.
b) The bond will be traded at par.
c) The bond will be traded below par.
d) The change in rate will not impact the price at which the bond is traded.
e) The bond could be traded below, at, or above par.
9.
Live Forever Life Insurance Company is selling a perpetuity contract that pays $1,550 monthly. The contract currently sells for $74,000.
a.
What is the monthly interest rate?
We need to find the interest rate that equates the perpetuity cash flows with the PV of
the cash flows. Using the PV of a perpetuity equation:
PV =
C
/
r
$74,000 = $1,550/
r
We can now solve for the interest rate as follows:
r
= $1,550/$74,000
r
= .0209, or 2.09% per month
b.
What is the APR?
The interest rate is 2.09% per month. To find the APR, we multiply this rate by the
number of months in a year, so:
APR = 12(2.09%)
APR = 25.14%
c.
What is the EAR?
Using the equation to find an EAR:
EAR = [1 + (APR/
m
)]
m
− 1
EAR = [1 + 0.0209]
12
− 1
EAR = .2824, or 28.24%
10. Given a market interest rate of 12 percent per year, what is the value at date t
= 4
(i.e., the end of year 4) of a perpetual stream of $50 annual payments that begin at
date t
= 10 (i.e., at the end of year 10 and continue forever)?
We have a perpetuity
r = 12%
C = $50
The payments begin at t=10
At the end of t=9, the value of the perpetuity is:
V
9
=
C
r
=
50
0.12
=
$
416.67
The value at t=4 of a cash flow of $416.67 at t=9 is:
V
4
=
$
416.67
(
1.12
)
5
=
$
236.43
11. The appropriate discount rate for the following cash flows is 7 percent
compounded quarterly.
Year
Cash Flow
1
$ 900
2
900
3
0
4
1,100
What is the present value of the cash flows?
The cash flows are annual and the compounding period is quarterly, so we need to calculate the EAR to make the interest rate comparable with the timing of the cash flows. Using the equation for the EAR, we get:
EAR = [1 + (APR/
m
)]
m
− 1
EAR = [1 + (.07/4)]
4
− 1
EAR = .0719, or 7.19%
And now we use the EAR to find the PV of each cash flow as a lump sum and add them together:
PV = $900/1.0719 + $900/1.0719
2
+ $1,100/1.0719
4
PV = $2,456.41
12. Your job pays you only once a year for all the work you did over the previous 12
months. Today, December 31, you just received your salary of $46,000 and you
plan to spend all of it. However, you want to start saving for retirement beginning
next year. You have decided that one year from today you will begin depositing 2
percent of your annual salary in an account that will earn 9 percent per year. Your
salary will increase at 6 percent per year throughout your career. How much
money will you have on the date of your retirement 41 years from today?
Since your salary grows at 6 percent per year, your salary next year will be:
Next year's salary = $46,000 (1 + .06)
Next year's salary = $48,760
This means your deposit next year will be:
Next year's deposit = $48,760(.02)
Next year's deposit = $975
Since your salary grows at 6 percent, you deposit will also grow at 6 percent. We can use
the present value of a growing perpetuity equation to find the value of your deposits
today. Doing so, we find:
PV
=
C
r
−
g
{
1
−
[
1
+
g
1
+
r
]
t
}
PV
=
$
975
.09
−
.06
{
1
−
[
1
+
.06
1
+
.09
]
41
}
PV = $22,154.61
Now, we can find the future value of this lump sum in 41 years. We find:
FV = PV(1 +
r
)
t
FV = $22,154.61(1 + .09)
41
FV = $758,491.28
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b. False
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1,500
Rate
Time (months)
2.5°%
7 months
a) $21.88
b) $39.96
c) $33.25
d) 20.25
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328.85
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uestion 1: Solve the following TVM problems using Excel formulas. You MUST use Excel formulas (FV or PV) to receive credit.
ou can assume that all payments are made at the beginning of the period and use "1" for the "type" argument in the formula.
A. Suppose you invest
11,400 today. What is the future value of the investment in
29 years, if interest at
7% is compounded annually?
B. Suppose you invest
$ 11,400 today. What is the future value of the investment in
29 years, if interest at
7% is compounded quarterly?
C. Suppose you invest
$
570 monthly. What is the future value of the investment in
29
29
years, if interest at
+
5% is compounded monthly?
5
6
7
8
19
20
21
22
23
24
25
26
27
28
29
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A
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P(t)=100(10)^.009
a. Evaluate P(0) and explain what it means in this context.
b. Approximately how many years will it take for the amount of money in your bank account to reach $120?
c. What year will you have $120 in your savings account?
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hapter 11 Lab Application
全 回
Sign ia
еBook
You have been depositing money into an account yearly based on the following investment amounts, rates and times, what is the value of that investment account at the end of that
period?
(Click here to see present value and future value tables)
Amounts of
Value at the End
Investment
Rate
Times
of the Period
$7,000
20%
16 years
612,094.91X
$11,000
15%
9 years
184,644.26X
$15,000
12%
5 years
95,292.71 X
$36,000
10%
2 years
75,600.00
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>
Check My Work
For each scenario, use the rate and time components to use the applicable time value of money table to determine the needed factor. Multiply the investment amount by the
future value factor to determine the value of end of the period.
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Number of periods?
Factor?
hapter
What is the amount of investment?
Problom 3
value of money and Бопа
X A P Q S Y
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your assumption and write it on the submitted file. [example: sa
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work paper.
Question 1
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True
OFalse
MacBook Pro
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F4
FS
F2
F3
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3
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please use IT-84 calculator
what is
N = I%= PV= PMT=FV= What are we solving for?
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QUESTION 1
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4.Q
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4. Present value
Finding a present value is the reverse of finding a future value.
is the process of calculating the present value of a cash flow or a series of cash flows to be received in the future.
Which of the following investments that pay will $10,500 in 13 years will have a lower price today?
O The security that earns an interest rate of 21.75%.
O The security that earns an interest rate of 14.50%.
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An investment that matures in four years
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(B) If you make a one-time deposit today of $800 you can earn 10% per year, how much would you have in your account after 15 years? Be sure to use cell
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(D) If you can earn 5% per year, precisely how many years would it take for your investment of $450 to turn into $1,200? Be sure to use cell references and
display your answer rounded to two places after the decimal point.
TIME VALUE OF MONEY: LUMP SUMS
PV
FV
r
n
(A)
(B)
(C)
(D)
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S407 at time
= 1 in years
$222 at time
= 2 in years
$426 at time = 3 in years
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4.
Find the interest rate implied by the following combinations of present and future values: (Round your answer to the nearest whole value.)
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Future Value
Intrest rate
A.
$400
11
$684
B.
$183
4
$249
C.
$300
7
$300
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Part 1 of 2
Points: 0 of 4
Save
Annual cash flows from two competing investment opportunities are given. Each investment opportunity will require the same initial investment.
E (Click the icon to view the competing investment opportunities.)
(Click the icon to view the Present Value of $1 table.) E (Click the icon to view the Present Value of Annuity of $1 table.)
Requirement
1. Assuming a 12% interest rate, which investment opportunity would you choose?
Begin by computing the present value of each investment opportunity. (Assume that the annual cash flows occur at the end of each year. If using present value ta-
use factor amounts rounded to three decimal places, X.XXX. Round intermediary computations and your final answer to the nearest whole dollar.)
The present value of investment opportunity A is
The present value of investment opportunity B is
Data table
Investment A Investment B
ok
Year 1
$
10,000 $
13,000
ok
Year 2
13,000
13,000
Year 3
16,000
13,000
$
39,000 $
39,000
Total…
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