Refresher - MATHEMATICS Quiz 12
PROBLEM 1:
The XYZ Company is contemplating the purchase of a new milling
machine. The purchase price of the new machine is $60000 and its
annual operating cost $2675.40. The machine has a life of seven years,
and it is expected to generate $15000 in revenue in each year of its life.
What is the net present value of the investment in this machine if the
interest rate is 8% per year?
Solution:
Net annual income = 15000 – 2675.40
Net annual income = $12,324.60
0 1 2 3 4 5 6 7
A A A A A A A = 12324.60
A ⎡⎣(1 + i)n - 1⎤⎦
P1 = P1
(1 + i)n i
12324.60 ⎡⎣(1.08)7 - 1⎤⎦
P1 =
(1.08)7 (0.08)
P1 = $64166.43
Net present value = 64166.43 - 600000
Net present value = $4166.43
, Refresher - MATHEMATICS Quiz 12
PROBLEM 2:
A landscape architect is designing an elliptical pool that will fit in the
center of a 20-by-30-foot rectangular garden, leaving at least 5 feet of
space on all sides. Find the equation of the ellipse.
Solution:
30
5’
5’ 5 5’
20
x
}
} 10
5’
y
a = 15 - 5 = 10
b = 10 - 5 = 5
x2 y2
2
+ 2 =1
a b
x2 y2
+ =1
100 25
PROBLEM 1:
The XYZ Company is contemplating the purchase of a new milling
machine. The purchase price of the new machine is $60000 and its
annual operating cost $2675.40. The machine has a life of seven years,
and it is expected to generate $15000 in revenue in each year of its life.
What is the net present value of the investment in this machine if the
interest rate is 8% per year?
Solution:
Net annual income = 15000 – 2675.40
Net annual income = $12,324.60
0 1 2 3 4 5 6 7
A A A A A A A = 12324.60
A ⎡⎣(1 + i)n - 1⎤⎦
P1 = P1
(1 + i)n i
12324.60 ⎡⎣(1.08)7 - 1⎤⎦
P1 =
(1.08)7 (0.08)
P1 = $64166.43
Net present value = 64166.43 - 600000
Net present value = $4166.43
, Refresher - MATHEMATICS Quiz 12
PROBLEM 2:
A landscape architect is designing an elliptical pool that will fit in the
center of a 20-by-30-foot rectangular garden, leaving at least 5 feet of
space on all sides. Find the equation of the ellipse.
Solution:
30
5’
5’ 5 5’
20
x
}
} 10
5’
y
a = 15 - 5 = 10
b = 10 - 5 = 5
x2 y2
2
+ 2 =1
a b
x2 y2
+ =1
100 25
