Exam
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Answer the question.
1)
A Japanese carmaker plans to expand its production in the United States. The company
borrowed $170 million for this expansion at an interest rate of 8% per year. The loan will
be repaid in equal payments at the end of each year over a 15–year period. What is the
amount of the annual payment?
1)
Answer:
$19,856,000.00
Explanation:
A =$170,000,000 (A/P, 8%, 15)
=$19,856,000.00
2)
Orlando International Airport plans to extend passenger capacity of its existing terminal to
accommodate its forecasted growth. A new terminal would be needed once the state’s
busiest airport reached 40 million passengers annually. Based on current growth rates,
Orlando International should reach the 40 million mark 11 years from now. The expansion
cost is expected to be $400 million. The airport service areas will also need attention. These
include passenger security checkpoints, ticketing lines, entering/exiting weaves, terminal
ramps, baggage claim, and baggage handling. Improvements in these areas will cost an
additional $240 million. How much does the airport need to set aside now to pay for these
costs, if the company can earn 10% per year, compounded every 4 months.
2)
Answer:
$216,832,000.00
Explanation:
Effective interest rate =(1 +r/M)M– 1 =(1+0.1/3)3–1
=0.1034 or 10.34% per year
P =$640,000,000 (P/F, 10.34%, 11)
=$216,832,000.00
3)
A major electronics manufacturer expects to generate additional revenue from its recently
won government contract. The company forecasts that the revenue will be $190 million in
the first year, but will decline by $2 million every year for the next 3 years. What is the
present worth of total revenue at an interest rate of 18% per year?
3)
Answer:
$504,153,400.00
Explanation:
P =$190,000,000 (P/A, 18%, 4) –$2,000,000 (P/G, 18%, 4)
=$504,153,400.00
4)
TransAtlantic Petroleum Corp. plans to seek two additional production licenses from the
Romanian government in addition to the three production licenses awarded to the
company last year. The company estimates the costs to drill, acquire the seismic data, and
conduct technical studies for these new fields will be $8.8 billion, 3 years from now. How
much will the company need to set aside now for these expenses if the company earns a
rate of return of 9% per year?
4)
Answer:
$6,795,360,000.00
Explanation:
P =$8,800,000,000 (P/F, 9%, 3)
=$6,795,360,000.00
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5)
Acme Corp. plans to expand its relationship with a soft drink manufacturer to make Acme
ready–to–drink coffee beverages available in Asia. The company wants to set aside $50
million now in its investment fund for the possible expansion 6 years from now. How
much will the company have in its investment account at the end of year 6, if the company
earns a rate of return of 8% per year?
5)
Answer:
$79,345,000.00
Explanation:
F =$50,000,000 (F/P, 8%, 6)
=$79,345,000.00
6)
How much would a company have to invest now in order to sufficiently provide for
annual payments of $313,000 over a 8–year period? Assume the interest rate is 12% per
year.
6)
Answer:
$1,554,858.80
Explanation:
P =$313,000 (P/A, 12%, 8)
=$1,554,858.80
7)
What is the amount of interest earned on $900 for 8 years at 10.5% simple interest per year?
7)
Answer:
$756.00
Explanation:
Simple interest (I) = Principal amount (P) x number of interest periods (N) x
interest rate per interest period (i)
P =$900; N =8; i =10.5%
I =$756.00
8)
Upon his employment at the age of 22, Robert began to make a series of equal year–end
deposits of $1100 to his retirement fund. After working for 5 years, he is now able to
increase his saving. He plans to increase his annual deposits to $2200, starting at the end of
next year (i.e., at the age of 28). He also intends to increase the amount by $400 each year
for the next 13 years (i.e. until the age of 41), and continue his equal deposits of $7400 each
year until the age of 60. He expects to retire at the age of 65. How much would his
retirement fund be worth at the time of his retirement if it earns a rate of return of 10% per
year?
8)
Answer:
$2,083,958.75
2
Explanation:
Partition the problem into three small problems and add the future worth
together.
First, find the future worth of the early annual deposits of $1100 from year 22 to
year 27, and move to year 65 with F/P factor.
At t =27, F1 = ($1100)(F/A, 10%, 6)
=$8487.16
At t = 65, F1 =$8487.16 (F/P, 10%, 38)
=$317,456.28
Second, find the future worth of the gradient deposits from year 28 to year 40,
and move to year 65 with the F/P factor.
At t =40,
F2 = ($2200)(F/A, 10%, 13) +$400 (P/G, 10%, 13)(F/P, 10%, 13)
=$100,041.18
At t = 65,
F2 =$100,041.18 (F/P, 10%,25)
F2 =$1,083,916.17
Third, find the future worth of the remaining equal deposit of $7400 from year
41 to year 60, and move to year 65 with the F/P factor.
At t= 60, F3 = ($7400)(F/A, 10%, 20)
=$423,835.00
At t = 65, F3 =$423,835.00 (F/P, 10%, 5)
=$682,586.27
Thus, the future of the fund at the age of 65 is:
F = F1 + F2 + F3
=$2,083,958.72
9)
Longhorn Fabricators Inc. plans to expand its metals–forming facility over the next 5 years.
The company will add 20,000 square feet to its 100,000–square–foot plant as it adds robotic
welding units, additional laser technology, and automated loading facilities. Construction
at the plant is expected to start by the end of next year. The company expects to pay 5
equal payments of $250,000 every 12 months over the 5 year period. What is the future
value of the total improvement cost, if the interest rate is 18% per year, compounded every
12 months?
9)
Answer:
$1,788,550.00
Explanation:
Effective interest rate =(1 +r/M)M– 1 =(1 +0.1800)1–1
=0.18 or 18.00 per 12 months
F =$250,000 (F/A, 18.00%, 5)
=$1,788,550.00
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10)
Acme Manufacturing Company is considering purchasing a maintenance contract for its
new waste management systems. Acme plans to begin the contract in year 5 and continue
through year 10. The cost of the contract is $11,300 per year, increasing by $300 each year.
If the company wishes to pre–pay the contract with uniform payments in year 1 through
year 5, what is the annual payment that Acme has to pay? Assume Acme’s minimum
attractive rate of return is 13% per year.
Answer:
$8325.10
Explanation:
Find the present worth at time 0 of the contract, and then find the annual
payment with A/P factor.
P = [$11,300 (P/A, 13%, 6) +$300 (P/G, 13%, 6)](P/F, 13%, 4)
=$29,282.80
A =$29,282.80 (A/P, 13%, 5)
=$8325.10
11)
Find the equivalent of present worth (t = 0) of a uniform series of $4550 for 8 years, if the
payment is made every 12 months, starting 6 years from now. Assume the interest rate is
12% per year, compound continuously.
Answer:
$12,086.17
Explanation:
Find the continuous compounding present value at year 5, and bring it back to
time 0 with continuous compounding present value with n =5.
The nominal interest per 12 months is 12.00%.
At t =7, P =$4550 (P/A, 12.00%, 8)
=$4550 (4.8402)
=$22,022.91
At t = 0, P =$22,022.91 (P/F, 12.00%, 5)
=$22,022.91 (0.5488)
=$12,086.17
12)
How many years will it take for an investment of $A to increase to $8A if the interest rate is
9% per year?
Answer:
25 years
Explanation:
Find the value of N from:
8A = A (F/P, 9%, N) =A (1 +0.09)N
log (8) = N log (1.09)
N =25
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13)
What value of G makes the two series of cash flows described below equivalent at an
interest rate of 3% per year, compounded every 3 months?
A: 22 annual deposits in the amount of $400
B: 11 annual deposits in the amount of $400 in the first year, and increasing by $G each
year.
Answer:
$61.26
Explanation:
Effective interest rate =(1 +r/M)M– 1 =(1 +0.03/4)4–1
=0.0303 or 3.03% per year
Equate the present worth of both cash flows and solve for G.
Present worth of A
=$400 (P/A, 3.03%, 22)
=$400 (15.8891)
=$6355.64
Present worth of B
=$400 (P/A, 3.03%, 11) + $G (P/G, 3.03%, 11)
=$400 (9.2373) + $G (43.4340)
Thus, G = [$6355.64 –$3694.92]/43.4340
=$61.26
14)
Susan made 4 uniform annual deposits of $1800 in a savings account that earned an
interest rate of 2% per year. Her last deposit was made 7 years ago. What is the future
value of her savings 13 years from now, if she leaves the account untouched?
Answer:
$11,023.71
Explanation:
Find the future worth of uniform annual deposits at year –7 with an F/A factor.
This will become the present value to move to the end of year 13 with an F/P
factor.
At t = (–7):
F =$1800 (F/A, 2%, 4)
=$7418.88
At t = (13):
F =$7418.88 (F/P, 2%, 20)
=$11,023.71
15)
Costs for maintaining buildings at an industrial complex over a 13–year period are
expected to be $5400 in year 1, increasing at the rate of 15% per year through year 13. At
an interest rate of 15% per year, what present worth (at time 0) is equivalent to the series of
maintenance costs?
Answer:
$61,043.48
Explanation:
Because f= i, P = (5400)(13) (P/F,15%, 1) =$61,043.48
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16)
An Australian–based energy drink manufacturer plans to expand its international markets
to the untapped East–Asian region. The company expects that the expansion will bring
additional net income of $30 million in the first year of the operation and amounts
increasing by $4.5 million for the next 8 years. What is the annual equivalent amount of
the net income at an interest rate of 13% per year?
Answer:
$44,406,300.00
Explanation:
A =$30,000,000 +$4,500,000 (A/G, 13%, 9)
=$44,406,300.00
17)
Find the 7 uniform annual deposits that can provide a single withdrawal of $38,500, 2
years after the last deposit is made at an interest rate of 5% per year.
Answer:
$4288.11
Explanation:
Find the present worth of the withdrawal at the last year of the deposit with a
P/F factor, and then find uniform annual deposits with an A/F factor.
At time 7:
P =$38,500 (P/F, 5%, 2)
=$34,919.50
A =$34,919.50 (A/F, 5%, 7)
=$4288.11
18)
Barney’s Liquids and Aunt Bee’s Lemonade plan to expand their international partnership
for the marketing and distribution of ready–to–drink tea products by adding 11 countries
to their current markets. If the agreement is reached, operations are expected to begin 2
years from now. The snack and beverage company forecasts that the agreement will bring
additional revenue of $80 million in the first year of the operation (i.e., the end of year 3),
with amounts increasing by $2.5 million each year for the next 7 years. What is the present
value now (t =0) of the total revenue if the interest rate of 17% per year?
Answer:
$266,590,313.62
Explanation:
Find the present worth of the revenue and bring it back to time 0.
At t = 2,
P2 =$80,000,000 (P/A,17%, 8) +$2,500,000 (P/G, 17%, 8)
=$364,942,250.00
At t = 0,
P = P2 (P/F, 17%, 2)
=$266,590,313.62
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