CE 39 MODULE 1 – ENGINEERING ECONOMY
Xavier University - Ateneo de Cagayan (Civil Engineering)
SIMPLE INTEREST
ANNUITY
1. If someone borrowed money from a lender with
a simple interest rate of 12%, determine the present
worth of Php 75,000.00, which is due at the end of
seven months.
Ans: Php 70,093
1. If Php 500 is invested at the end of each year for
4 years at an annual interest rate of 10%, what is
the total peso amount upon the deposit of the
fourth payment?
Ans: Php 2,320.50
2. Leo has invested Php 1,000.00, part at 5% and
the remainder at 10% simple interest. How much is
invested at higher rate if the total annual interest
from this investment is Php 95.00?
Ans: Php 900
2. A man paid 10% as down payment of Php 200k
for a house and lot and agreed to pay the balance
on monthly installments for 5 years at an interest
rate of 15%, compounded monthly. What was the
monthly installment in pesos?
Ans: Php 42,821.87
3. You borrowed Php 120,000.00 from a friend and
promised to pay 6% simple interest. How much will
you pay at the end of 1 year and 6 months?
Ans: Php 130,800
4. A man borrowed from a bank under a promissory
note that he signed in the amount of Php 60,000 for
a period of one year. He received only Php 50,150
after the bank collected the advanced interest
and an additional amount of Php 850 for notarial
and inspection fees. What was the rate of simple
interest that the bank collected in advance?
Ans: 17.65%
COMPOUND INTEREST
1. If the sum of Php 12,000 is deposited in an
account earning an interest rate of 9%
compounded quarterly, what will it become after
1 year?
Ans: Php 13,116.99
2. How many years are required for Php 1,000 to
increase to Php 2,000 if invested at 9% per year
compounded continuously?
Ans: 7.70 years
3. What payment ten years from now is equivalent
to a payment of Php 1,000 six years from now, if
interest is 15% compounded monthly?
Ans: Php 1,815.35
4. What rate in percent compounded monthly is
equivalent to 18 % compounded semi-annually?
Ans: 17.36%
5. An investment of Php 3M earns interest of 9%
compounded continuously. What is the effective
rate of interest?
Ans: 9.417%
3. An investor deposits Php 10,000 at the end of
each year in an account which gives a nominal
annual interest of 5% compounded continuously.
How much sum will he accumulate in 10 years?
Ans: Php 126,528
4. An engineer has just borrowed Php 800,000 from
a local bank, at the rate of 1% per month on the
unpaid balance. His contract states that he must
repay the loan in 36 equal monthly installments.
How much money must he repay each month?
(Disregard this Problem)
5. A father wants to set aside money for his 5-yearold son’s future college education. Money can be
deposited in a bank account that pays 8% per
year, compounded annually. What equal deposits
should be made by the father on his son’s 6th
through 17th birthdays, in order to provide
Php 80,000 on his son’s 18th, 19th, 20th, and
21st birthdays?
Ans: Php 13,962.60
6. A fund is to provide an annual scholarship at
Php 4,000 for the first 5 years; Php 6,000 for the next
5 years and Php 9,000 thereafter. The fund will be
established 1 year before the first scholarship is
awarded. If the fund earns 12% interest, what sum
must be deposited?
Ans: Php 50,840
CAPITALIZED COST AND ANNUAL COST
1. Compute the capitalized cost of a new car
worth Php 800,000 if it is estimated that it requires
Php 20,000 per year to maintain and must be
replaced at the same amount with a salvage
value of Php 300,000 after 5 years if the interest rate
is 12% per annum.
Ans: Php 1,622,540.55
CE 39 MODULE 1 – ENGINEERING ECONOMY
Xavier University - Ateneo de Cagayan (Civil Engineering)
2. A contractor can buy dump trucks for
Php 800,000 each or rent them for Php 1200 per
day. The truck has a salvage value of Php 100,000
at the end of its useful life of 5 years. The annual
cost of maintenance is Php 20,000. Using the
annual cost method and 14% interest rate,
determine the number of days to warrant its
purchase.
Ans: 199
Situation 1 (3-5)
A manufacturing plant installed a new boiler at a
total cost of Php 150,000. It is estimated to have a
useful life of ten years with the scrap value of Php
5,000. Annual maintenance cost is Php 10,000. If
the interest is 12% compounded annually:
3. Determine the equivalent present worth of the
annual maintenance cost.
Ans: Php 83,333.33
4. Determine the equivalent annual cost of the net
amount required to replace the boiler.
Ans: Php 8,262.70
5. Determine its capitalized cost.
Ans: Php 302,189.20
DEPRECIATION
1. A sand mill costs Php 410,000. Salvage value of
the mill is estimated to be Php 60,000 after 20 years.
Find the appraisal or book value of the sand mill
using straight line depreciation method after
10 years.
Ans: Php 235,000
2. A machine costing Php 1.8M has a salvage value
of Php 300,000 after 5 years. Calculate the
depreciation value (book value) at the end of 3
years using the straight-line method.
Ans: Php 900,000
3. A dump truck was bought for Php 300,000 six
years ago. It will have a salvage value of Php
30,000 four years from now. Determine the present
value of the dump truck if the depreciation
method used is sinking fund at 6%.
Ans: Php 157,115
4. A machine costs Php 100,000 with a salvage
value of Php 20,000 at the end of its life of 8 years.
What is the depreciation at the 6th year using
Sinking Fund method if money is worth 6%
annually?
Ans: Php 8,082.88
5. An asset is purchased for Php 9,000. Its estimated
life is 10 years, after which it will be sold for Php
1,000. Find the book value at the end of third year
if sum-of-the-year’s digit method (SOYDM)
depreciation is used.
Ans: Php 5,703
6. An equipment costs Php 1,200,000. At the end of
its economic life of 5 years, its salvage value is Php
300,000. Using sum of the years digit method, what
will be its book value on the 3rd year?
Ans: Php 480,000
7. XU purchased new 3D projectors with a total
worth of Php 618,000. If the equipment is
depreciated over an eight-year period with
salvage value of 5%, determine the depreciation
charge during the fifth year using declining
balance method.
Ans: Php 302,189.20
8. A machine has a first cost of Php 73,500 and a
salvage value of Php 3,500 at the end of its useful
life of 8 years. Evaluate the depreciation of the
machine during the 5th year using Matheson’s
Method (declining balance method).
Ans: Php 5077
CE 39 MODULE 1 – ENGINEERING ECONOMY
Xavier University - Ateneo de Cagayan (Civil Engineering)
MSTE REVIEW
1. The height of the cone (vertex up) is H. It contains
water to a depth of 2/3H. What is the ratio of the
volume of water to that of the cone? Ans 26:27
2. Three circles with radii 3.0, 5.0, and 9.0 cm are
externally tangent. What is the area of the triangle
formed by joining their centers? Ans 47.91 cm2
3. If two angles are in the ratio of 3:2, find the angles
if they are adjacent and form an angle measuring
40o. Ans 16 and 24
4. A father and his son can dig a hole if the father
works 6 hours and his son works 12 hours, or they
can do it if the father works 12 hours and the son
works 8 hours. How long will it take for the father to
dig the hole alone? Ans 24 hours
5. An inverted conical container has a diameter of
40 in and a depth of 15 in. If water is flowing out of
the vertex of the container at a rate of 25π in3/sec,
how fast is the depth of the water dropping when
the height is 5 inches? Ans 9/16 in/sec
HYDRAULICS REVIEW
Situation (1-3)
A vertical gate 0.60 m wide and 1.2 m high is
submerged completely in water with its top edge
flushed with the water surface.
1. Find the magnitude of the total force acting on
one side of the gate, in kN. Ans 4.238 kN
2. Calculate the distance between the location of
the total pressure and the center of the gate.
Ans 200 mm
3. Calculate the distance between the location of
the total pressure and the surface of the water.
Ans 800 mm