TAKE HOME EXAMINATION 6 (DIFFERENTIAL PROBLEM 5: PROBLEM 9:

CALCULUS) If the radius of a circle increases at a rate of 0.01 cm/s, Evaluate dy/dx when x = 2 for the function f(x) =
find the rate of change of the area when the radius is 3 (a+bx²)/x² .
PROBLEM 1:
cm long. a. -a/2
A man on a wharf is pulling a rope tied to a raft at a rate
a. 3.19 cm²/s b. -a/3
of 0.6 m/s. If the hands of the rope are 3.66 m above the
b. 2.19 cm²/s c. -a/4
water, how fast is the raft approaching the wharf when
c. 1.19 cm²/s d. a/4
there are 6.10 m of rope out?
d. 0.19 cm²/s
a. 1.75 m/s
PROBLEM 10:
b. 0.75 m/s
PROBLEM 6: Find the value of x for which the rate of change of y with
c. 0.25 m/s
Determine the derivative of the change of the volume of respect to x is 6 for the function y = x times the square
d. 0.54 m/s
a sphere with respect to its radius when the radius is 6 root of x.
inches. a. ±2
PROBLEM 2:
a. 144 π b. ±3
If the distance y from the origin at time t is given by y=-
b. 155 π c. ±1
16t²+ 3000t + 50 000, what is the initial velocity of the
c. 166 π d. ±4
object?
d. 177 π
a. 3000
PROBLEM 11:
b. 53 000
PROBLEM 7: If the surface of the water in a vertical cylindrical tank is
c. 0
If the radius of a circle increases at a rate of 0.09 cm/s, rising at the rate of 12.75 cm per minute when water is
d. 50 000
find the rate of change in cm2/s of the area when the flowing into the tank at the rate of 5.60 liters per minute,
radius is 3 cm long. what is the diameter of the tank?
PROBLEM 3:
* a. 23.65 cm
A stone is thrown into still water and causes concentric
1 point b. 18.92 cm
circular ripples. The radius of the ripples increases at the
a. 3.194 c. 20.48 cm
rate of 10 inches/sec. At what rate does the area of the
b. 1.696 d. 21.56 cm
ripples increases when its radius in 3 inches?(in sq.
c. 1.192
inch/sec)
d. 2.193 PROBLEM 12:
a. 125.2 in²/s
Two posts, 2.4 m and 3.6 m high, stand 4.5 m apart. They
b. 288.1 in²/s
PROBLEM 8: are to be stayed by two wires attached to a single stake,
c. 188.5 in²/s
If the area of a circle increases at a rate of 6 cm²/s, find located between the two posts at ground level and
d. 208.3 in²/s
the rate of change in cm/s of the radius when the r is 4 running to the tops of the posts. Where should the stake
cm long. be placed to use the least amount of wire?
PROBLEM 4:
a. 0.19 cm/s a. 1.2 m
A publisher estimates that t months after he introduces a
b. 0.69 cm/s b. 1.8 m
new magazine, the circulation will be C(t) = 150t² + 300t
c. 0.24 cm/s c. 0.6 m
+ 6000 copies. If this prediction is correct, how fast will
d. 0.20 cm/s d. 2.3 m
the circulation increase 7 months after the magazine is
introduced?(copies/month)
a. 1400
b. 2400
c. 2100
d. 3300
PROBLEM 13: PROBLEM 17:
Water is poured into a cylindrical tank at a rate of 10 ft³/s. Find the maximum area of a rectangle inscribed in a PROBLEM 22:
Find the radius if the rate at which water level is rising is semi-circle with radius of 10. A cable is to run from a power plant on one side of a
4 inches per second. a. 110 m² river 900m wide to a factory on the other side 3 km away
a. 3.1 b. 80 m² upstream. The cost of running the cable on land is $4
b. 2.3 c. 100 m² per meter while the cost under water is $5 per meter.
c. 1.2 d. 90 m² Find the length of cable, x on land for most economical
d. 4.1 cost.
PROBLEM 18: a. 1800 m
PROBLEM 14: Find the weight of the heaviest circular cone that can be b. 1600 m
A cylinder with radius “R” meter and 10m high is filled cut from a 150 N sphere. c. 2000 m
with water at the rate of 1m³/min. How fast is the water a. 44.44 N d. 1400 m
rising in the cylinder if it is in vertical position? b. 40.36 N PROBLEM 23:
a. 1/πR² c. 35.25 N A light at eye level stands 20 ft. from a house and 15 ft.
b. 10πR d. 30.78 N from the path leading from the house to the street. A
c. πR² man walks along the path at 6 fps. How fast does his
d. π²R PROBLEM 19: shadow move along the wall when he is 5 ft. from the
A lot is in the shape of a quadrant of a circle of radius 100 house.
PROBLEM 15: meters. Find the area of the largest rectangular building a. 7 ft/s
A three-meter steel pipe is leaning against a vertical wall that can be constructed inside the lot. b. 8 ft/s
and the other end is on the horizontal floor .If the lower a. 5000 m² c. 4 ft/s
end slides away from the wall at the rate of 2 cm/s, how b. 5050 m² d. 6 ft/s
fast the upper end is sliding down when the lower end is c. 5500 m² PROBLEM 24:
2 m away from the wall? d. 4950 m² The top of a 30 feet ladder, leaning against a vertical wall
a. 3.561 cm/s is slipping down at the rate of 2.5 ft./s. Find how fast is
b. 1.789 cm/s SITUATION 1: the bottom end of the ladder slipping along the ground
c. 1.235 cm/s A balloon is released from the ground 150 m from the when it is 10 feet away from the base of the wall?
d. 2.563 cm/s observer. The balloon rises directly upward at the rate of a. 8.01
3 m/sec. b. 6.03
PROBLEM 16: 20. How far from the observer is the balloon 10 c. 7.07
The total cost of producing gifts could be express by the seconds later in m? d. 4.05
function C = 60 x² – 0.01x³ where x is the number of gifts a. 115.36 PROBLEM 25:
produced. Determine the value of x so that the average b. 152.97 Find the area of the largest rectangle with the lower base
unit cost is minimum. c. 126.58 on the X–axis and the upper vertices on the parabola y =
a. 2000 d. 143.75 12 – x².
b. 3000 a. 32 sq.units
c. 4000 21. How fast is the balloon moving away from the b. 30 sq.units
d. 5000 observer 10 seconds later? c. 36 sq.units
a. 0.588 d. 34 sq.units
b. 0.275 PROBLEM 26:
c. 0.725
d. 0.835
A closed box is to be made of a piece of aluminum 25 cm b. 42 PROBLEM 36:
by 40 cm by cutting pieces out. Determine the maximum c. 35 Water is poured into a cylindrical tank at a rate of 10 ft³/s.
capacity of the box. d. 12 Find the radius if the rate at which water level is rising is
a. 1458 cu.cm PROBLEM 32: 4 inches per second.
b. 1641 cu.cm A certain association was established in 1975. The a. 2 ft
c. 1389 cu.cm membership is in a function f(x) = 2x³ – 45x² + 264x b. 3 ft
d. 1539 cu.cm where x is the number in years. In what year will the c. 4 ft
PROBLEM 27: members is minimum? d. 5 ft
If the surface of the water in a vertical cylindrical tank is a. 1984
rising at the rate of 12.75 cm/min when water is flowing b. 1986 PROBLEM 37:
into the tank at the rate of 5.60 liters per minute, what is c. 1985 Find the length of the arc of the curve defined by y = (x +
the diameter of the tank? d. 1983 1)³′² between the points (-1,0) and (4,5³′²).
a. 23.65 cm PROBLEM 33: a. 250/15
b. 19.02 cm Compute the slope of the curve x² + 2y² + 2x – 5 = 0 at (1, b. 300/18
c. 18.25 cm 1). c. 290/20
d. 21.45 cm a. 3/4 d. 335/27
b. -1
PROBLEM 28: c. 2 PROBLEM 38:
Find the curvature of y = x³ at (1, 1). d. -1/2 Find the area of the largest piece of rectangular ground
a. 0.165 PROBLEM 34: that can be enclosed by 100 m fencing, if part of an
b. 0.189 A balloon is rising vertically over a point A on the ground existing straight wall is used as one side.
c. 0.584 at the rate of 15 ft./sec. A point B on the ground is level a. 1247 m²
d. 0.367 with A and is 30 ft. from A. When the balloon is 40 ft. b. 1250 m²
PROBLEM 29: from A, at what rate is its distance from B changing? c. 1249 m²
Evaluate the limit of (x² – 1)/(x² + 2x – 3) as x approaches a. 12 ft./sec. d. 1248 m²
to 1. b. 13 ft./sec.
a. 1/2 c. 15 ft./sec. PROBLEM 39:
b. 3/2 d. 10 ft./sec. Find the slope of the line tangent to the curve y = e ^(4x)
c. 2/3 at x = 0.
d. 2/5 PROBLEM 35: a. 2
PROBLEM 30: A search light from a lighthouse 2km off shore is b. 3
Find the rate at which the volume of a right circular following a car traveling along the shore. When the car is c. 4
cylinder of constant altitude 10 feet changes with respect 1 km from the point on the shore nearest to the d. 5
to its diameter when the radius is 15 feet. lighthouse, the search light is rotating at the rate of 0.25
a. 130π ft³/ft revolution per hour. Compute the velocity of the car at SITUATION 2:
b. 140π ft³/ft that instant. Given the curve y = 6(4 + x)^(½).
c. 150π ft³/ft a. 3.93 kph 40. Determine the equation of tangent of the curve at
d. 160π ft³/ft b. 5.18 kph point (0, 12).
PROBLEM 31: c. 3.81 kph a. 3x - 2y - 24 = 0
Evaluate the limit of x² + 3x - 4 as x approaches the value d. 1.21 kph b. 3x + 3y – 36 = 0
of 4 c. 3x + 2y - 24 = 0
a. 24 d. 3x - 2y + 24 = 0
41. Find the curvature at point (0, 12). c. 16
a. 31.25 d. 4
b. 9.02 PROBLEM 47:
c. 0.125 A semi-circle of radius 14 cm is formed from a piece of
d. 0.032 wire. If it is bent into a rectangle whose length is 1 cm
more than its width, find the area of the rectangle?
42. Determine the coordinate of the center of curvature a. 323.57 cm²
at point (0, 12). b. 235.12 cm²
a. (-26, 16/3) c. 425.76 cm²
b. (26, 16/3) d. 120.70 cm²
c. (-26, -16/3)
d. (26, -16/3) PROBLEM 48:
The diagonals of a parallelogram are 376.14 cm and
SITUATION 3: 427.21 cm and the included angle is 70º12’38’’. Find the
Water is flowing at the rate of 16-cm³/s into a conical length of the sides.
vessel 24 cm deep and having a radius of 6 cm across the a. 145.75 cm
base. b. 231.94 cm
43. How fast the water is rising when water is 12 cm c. 345.12 cm
deep above the vertex? d. 198.12 cm
a. 0.366 cm/s
b. 0.466 cm/s SITUATION 4:
c. 0.566 cm/s If the smaller side of a rectangle is increased by 3 m, and
d. 0.628 cm/s the larger side by 5 m, one dimension becomes 3/5 of
44. How fast the wetted surface area of cone is the other, and the area is increased by 135 square
increasing when water is 12 cm deep above the vertex? meters.
a. 10.997 cm²/s 49. Find the larger original side.
b. 19.097 cm²/s a. 15 m
c. 17.099 cm²/s b. 20 m
d. 14.997 cm²/s c. 25 m
d. 8 m
45. How fast the water is rising when water is 12 cm
deep above the base? (i. e. the cone is inverted) 50. Find the difference between the sides.
a. 0.366 cm/s a. 15 m
b. 0.466 cm/s b. 20 m
c. 0.566 cm/s c. 25 m
d. 0.628 cm/s d. 8 m
PROBLEM 46:
If x and y are positive real numbers; x, -4, y form a
geometric progression and 14, x, y form an arithmetic
progression. Determine y.
a. 2
b. 8
TAKE HOME EXAMINATION 7 (INTEGRAL Compute the area bounded by the curve y² = 4x and y² = PROBLEM 11:
CALCULUS) 8x – 8. Find the area bounded by y =√(11-x) , the lines x = 2 and
a. 4.56 sq.units x = 10, and the X-axis.
PROBLEM 1: b. 3.77 sq.units a. 15.78
Find the volume generated by rotating the region c. 2.67 sq.units b. 20.47
bounded y = x, x = 1 and y₁² = 4x about the X – axis. d. 1.69 sq.units c. 18.59
a. 5/3 pi PROBLEM 7: d. 17.33
b. 7/3 pi Given is the area in the first quadrant bounded by the PROBLEM 12:
c. 4/3 pi curve x²= 8y, the line y –2 = 0 and the line x = 0 Find the area bounded by y = x² – 4x + 5 and y = 2x – 3.
d. 11/3 pi .Compute the moment of inertia about the y – axis. a. 5/6
PROBLEM 2: a. 23.05 b. 4/3
Find the area bounded by y = 2x + x² – x³, the x-axis, and b. 18.04 c. 2/3
the lines x = -1 and x = 1. c. 17.07 d. 1/2
a. 3/2 d. 14.04 PROBLEM 13:
b. 1/4 PROBLEM 8: Find the area of surface of revolution generated by
c. 2/3 Find the area of the region bounded by y = x²/4 and y = revolving the line 3y = 4x from x = 0 to x = 3 about the x-
d. 3/5 x/2 + 2. axis.
PROBLEM 3: a. 9 a. 23π
b. 10 b. 17π
c. 6 c. 20π
d. 12 d. 42π
PROBLEM 9: PROBLEM 14:
Find the volume of the solid generated by rotating about Find the area bounded by the parabola x² – 4x + 12y – 20
the x-axis the region bounded by the curves y = x³, x = 2 = 0 and the x-axis between x = 1, x = 2.
a. 3/5 and x-axis. a. 1.65
b. 2/3 a. 116π/7 b. 1.38
c. 1/4 b. 128π/7 c. 1.97
d. 3/2 c. 205π/7 d. 1.85
PROBLEM 4: d. 105π/7 PROBLEM 15:
Find the area bounded by y = (11 – x)^(1/2) , the lines 3x PROBLEM 10: Find the volume of the solid generated by revolving
= 2 and x = 10 and the x-axis. The cross section of a trough is a parabolic segment 8 ft. about y = 2 the region bounded by y² = 2x, x = 8, and y =
a. 21.478 sq.units wide and 4 ft. deep. If the trough is filled with a liquid 2.
b. 20.567 sq.units weighing 45 lb/ft³, find the total force on one end. a. 30π/3
c. 22.567 sq.units a. 1653 lb b. 28π/3
d. 19.456 sq.units b. 1536 lb c. 32π/3
PROBLEM 5: c. 1563 lb d. 26π/3
Evaluate the integral of sin⁴θdθ from θ = 0 to θ = π/2 d. 1356 lb SITUATION 2
a. 3π/16 Consider the two curves: x² + y² = 48 and x² + 8y = 0.
b. 2π/9 16. Determine the length of the line AB. A and B
c. 5π/8 are points of intersection.
d. 4π/15 a. 8
PROBLEM 6: b. 11.30
c. 5.65 SITUATION 6: c. 13.53 cu.units
d. 13.86 Given in the curve y = x²/4 and the line x = y. d. 53.31 sq.units
17. Determine the area bounded. 22. Find the distance from the origin to the point of PROBLEM 29:
a. 23.23 intersection Find the volume of the solid generated by revolving
b. 30.17 a. 5.66 units about the x-axis the smaller area bounded by the circle x²
c. 83.62 b. 4.25 units + y² = 2 and the semi-cubical parabola y³ = x².
d. 66.67 c. 3.57 units a. 6.77
d. 6.33 units b. 7.78
PROBLEM 18: 23. Find the area bounded by the curve and the given c. 5.67
Find the area bounded by the line x – 2y + 10 = 0, the x- line. d. 9.68
axis, the y-axis and x = 10. a. 2.667 sq.units PROBLEM 30:
a. 75 b. 3.564 sq.units Determine the moment of inertia with respect to the x –
b. 65 c. 1.358 sq.units axis of the area in the first quadrant bounded by the
c. 85 d. 4.258 sq.units curve y² = 4x, the line y = 4 and the y axis.
d. 95 24. Find the area bounded by the curve, the x-axis and a. 51.2
PROBLEM 19: line x = 4. b. 45.6
The area bounded by the curve y = 2x^(1/2), the line y= 6 a. 5.33 sq.units c. 25.8
and the y-axis is to be revolved at y= 6. Determine the b. 6.33 sq.units d. 56.8
centroid of the volume generated. c. 4.33 sq.units SITUATION 5:
a. 2.10 d. 3.33 sq.units Given the curve r = 4(1 – sinθ )
b. 1.40 PROBLEM 25: 31. Determine the area bounded.
c. 1.80 Find the area bounded by x² = 2 – y and x + y = 0. a. 32 π
d. 1.25 a. 3.67 sq.units b. 24 π
PROBLEM 20: b. 4.50 sq.units c. 16 π
Find the area bounded by the curve defined by the c. 2.45 sq.units d. 8 π
equation x² = 8y and its latus rectum. d. 1.33 sq.units 32. Determine the perimeter.
a. 12.45 sq. units SITUATION 3: a. 9.37 units
b. 10.67 sq. units Given the curve y = 2x^(0.5) and line x = y. b. 16 units
c. 8.33 sq. units 26. Compute the area bounded. c. 18.74 units
d. 7.86 sq. units a. 3.235 sq. units d. 32 units
PROBLEM 21: b. 2.667 sq. units SITUATION 8:
Find the area of the surface generated by revolving the c. 1.457 sq. units Given the area bounded by the curve y²= 4x and y² = 8x –
line 3y = 4x about the x –axis when x = 0 to x = 3. d. 4.759 sq. units 8.
a. 31.42 sq. units 27. Compute the distance from the x-axis to the centroid. 33. Compute the area bounded by the two curves.
b. 62.83 sq. unIts a. 2.0 a. 4.56 sq.units
c. 47.12 sq. units b. 1.5 b. 3.77 sq.units
d. 78.54 sq. units c. 3.5 c. 2.67 sq.units
d. 2.5 d. 1.69 sq.units
28. Compute the volume generated if the area bounded 34. Determine the centroid of the area bounded by the
is to be revolved about x –axis. two curves.
a. 33.51 cu.units a. (0.6, 0)
b. 35.31 sq.units b. (0.8, 0)
c. (1.8, 0) PROBLEM 40: d. 4950 m²
d. (2, 0) Find the volume of the solid when the region enclosed by PROBLEM 46:
35. Determine the perimeter of the area bounded by the the given curves, y=x², x= y² is revolved about the y-axis. An automatic garden spray produces a spray to a
two curves. a. 5π/8 distance of 1.8 m and revolves through an angle α which
a. 13.3 units b. 6π/5 may be varied. If the desired spray catchment area is to
b. 6.65 units c. 4π/9 be 2.5 m², to what should angle α be set?
c. 7.20 units d. 3π/10 a. 84.8°
d. 9.36 units SITUATION 2: b. 85.2°
Given the equation of the curve y =0.01(1600 – x²). c. 88.4°
PROBLEM 36: 41. Find the area bounded by the curve and the x-axis. d. 87.8°
Find the area of the region in the first quadrant bounded a. 472.41 sq.units PROBLEM 47:
by the hyperbola x² – y²= 4 and one of its asymptotes, b. 853.33 sq.units Given the area in the first quadrant bounded by x² = 8y,
from x = 2 to x = 4. c. 652.14 sq.units the line y – 2 = 0 and the y-axis. What is the volume
a. 2.10 sq. units d. 341.20 sq.units generated when the area is revolved about the line y – 2
b. 3.14 sq. units 42. Find the moment of inertia with respect to the y-axis = 0?
c. 1.70 sq. units of the area bounded by the given curve and the x-axis. a. 31.12
d. 2.47 sq. units a. 13 166.67 units⁴ b. 21.47
PROBLEM 37: b. 71 152.20 units⁴ c. 29.86
Find the area enclosed by the curve y = sin 2x, the x – c. 87 102.12 units⁴ d. 26.81
axis and the ordinates x = 0 and x = π/3. d. 49 932.19 units⁴ PROBLEM 48:
a. 1/2 PROBLEM 43: Find the area enclosed by the curve x² + 8y + 16 = 0, the x
b. 5/8 The area in the 1st and 2nd quadrant bounded by the - axis, y - axis and the line x - 4 = 0.
c. 3/4 curve 4x² + 25y²= 100 is to be revolved about x-axis. a. 10.67 sq.units
d. 2/3 Compute the volume generated. b. 13.67 sq.units
PROBLEM 38: a. 83.77 cu.units c. 12.67 sq.units
Determine the area between the curve y = x³ – 2x² – 8x b. 85.33 cu.units d. 11.67 sq.units
and the x-axis. c. 87.33 cu.units PROBLEM 49:
a. 51.23 d. 95.45 cu.units A circular cylinder with a volume of 6.54 cu. m. is
b. 48.56 PROBLEM 44: circumscribed about a right prism whose base is an
c. 50.78 Find the volume bounded by the surface 2z = 4 – x² – y² equilateral triangle of side 1.25 m. What is the altitude of
d. 49.33 and the XY plane. the cylinder in m?
PROBLEM 39: a. 3π a. 6
Find the volume of the solid that results when the region b. 4π b. 4
bounded by y = 1/x, y = 2, and x = 2 is rotated about y – c. 5π c. 5
axis. d. 2π d. 3
a. 4.5π PROBLEM 45: PROBLEM 50:
b. 3.5π A lot is in the shape of a quadrant of a circle of radius 100 Find the area inside the cardioids r = 1 + sinθ and outside
c. 2.5π meters. Find the area of the largest rectangular building the circle r = 2 sinθ
d. 1.5π that can be constructed inside the lot. a. 3.25 sq. units
a. 5000 m² b. 8.54 sq. units
b. 5050 m² c. 5.54 sq. units
c. 5500 m² d. 1.57 sq. units
TAKE HOME EXAMINATION 12 (ENGINEERING d. 30% c. P8 504
ECONOMY 1) 6. What was the rate of interest for one year? d. P5 836
a. 18.58% PROBLEM 12:
b. 20.45% Determine the ordinary simple interest on Php 700 for 8
PROBLEM 1:
c. 27.15% months and 15 days if the rate of interest is 15%.
Determine the exact simple interest on P5000 for the
period from January 15 to June 20, 1993, if the rate of d. 33.33% a. P77.60
simple interest is 14%. PROBLEM 7: b. P42.45
a. P430.95 In how many years will your money be doubled if it earns c. P52.47
b. P285.85 12% interest compounded annually? d. P74.38
c. P305.71 a. 7.91 PROBLEM 13:
b. 6.88 A chemical engineer wishes to set up a special fund by
d. P299.18
c. 7.36 making uniform semi-annual end of period deposits for
PROBLEM 2:
d. 6.12 20 years. The fund is to provide P100 000 at the end of
Determine the ordinary simple interest on P1200 for the
period from January 16 to November 26, 1992, if the rate PROBLEM 8: each of the last five years of the 20 year period. If
of interest is 24%. At a certain interest rate compounded quarterly, P1000 interest is 8% compounded semi-annually, what is the
a. P252 will amount to P4500 in 15 years. What is the amount at required semi-annual deposit to be made?
b. P258 the end of 10 years? a. P6 193.39
c. P225 a. P4245.12 b. P7 025.45
d. P245 b. P3878.23 c. P5 068.59
c. P1345.16 d. P8 306.12
PROBLEM 3:
A man borrows P10 000 from a loan firm. The rate of d. P2725.17 SITUATION 2:
simple interest is 15%, but the interest is to be deducted PROBLEM 9: Aidan invests $5000 in an account that earns 3.5%
from the loan at the time the money is borrowed. At the In how many years will your money be doubled if it earns interest compounded continuously.
end of one year he has to pay back P10 000. What is the 12% interest compounded annually? 14. What is the total amount of his investment after 3
actual rate of interest? a. 7.91 years?
b. 6.88 a. 4777.11
a. 14.88%
c. 7.36 b. 5003.52
b. 12.58%
c. 17.65% d. 6.12 c. 3555.3
d. 11.74% PROBLEM 10: d. 5553.55
SITUATION 1: What is the present worth of a 10 year annuity paying 15. How long will take him to earn $15000
A man borrowed P5000 from a bank and agreed to pay P10 000 at the end of each year, with interest at 15% a.19. 7
the loan at the end of 9 months. The bank discounted compounded annually? b. 31.4
a. P46 300 c. 41.23
the loan and gave him P4000 in cash.
b. P50 188 d. 24.3
4. What was the rate of discount?
c. P40 078 PROBLEM 16:
a. 20%
b. 28% d. P51 448 Find the nominal rate which if converted quarterly could
c. 25% PROBLEM 11: be used instead of 12% compounded monthly.
d. 30% What is the present worth of P500 deposited at the end a. 10.36%
5. What was the rate of interest? of every three months for 6 years if the interest is 12% b. 9.58%
a. 20% compounded semi-annually? c. 12.12%
a. P6 205 d. 8.25%
b. 28%
b. P7 560
c. 25%
SITUATION 3: PROBLEM 22: 26. For how many years starting July 1, 1988 can
An advertisement of an investment firm states that if you A man possesses a promissory note, due 3 years hence, scholarship be awarded?
invest P500 in their firm today you will get P1000 at the whose maturity value is P6700.48. If the rate of interest a. 12 years
end of 4 ½ years. is 10% compounded semi-annually, what is the value of b. 14 years
17. What nominal rate is implied if interest is this note now? c. 8 years
compounded monthly? a. P6 000 d. 10 years
a. 19.58% b. P4 000 27. What will be the balance in the fund after the last
b. 15.50% c. P5 000 award is made?
c. 13.15% d. P7 000 a. P4630.05
d. 12.55% PROBLEM 23: b. P1508.85
18. Determine the effective interest. A man expects to receive P 30,000 in 10 years. How c. P4780.36
a. 19.58% much is that money worth now considering interest at d. P1406.40
b. 10.458% 6% compounded quarterly? PROBLEM 28:
c. 16.653% a. 16537.87 A man paid a 10% down payment of P200,000 for a
d. 12.514% b. 11137.82 house and lot and agreed to pay the balance of monthly
PROBLEM 19: c. 12537.88 installments for 5 years at an interest rate of 15%
A man bought a lot worth P1 000 000 if paid in cash. On d. 18574.81 compounded monthly. What was the monthly
the installment basis, he paid a down payment of P200 PROBLEM 24: installment in pesos?
000; P300 000 at the end of one year; P400 000 at the Determine the ordinary simple interest on P10, 000 for a. Php 44,728.78
end of three years and a final payment at the end of five 10 months and 9 days if the rate interest is 12%? b. Php 42,821.87
years. What was the final payment if interest was 20%. a. 2050 c. Php 41,727.82
a. P460 835 b. 1030 d. Php 48,265.29
b. P670 350 c. 980 PROBLEM 29:
c. P760 781 d. 2000 Annual deposits were made in a fund earning 10% per
d. P792 560 PROBLEM 25: annum. The first deposit was P2000 and each deposit
PROBLEM 20: If you borrow money from your friend at 12% simple thereafter was P200 less than the preceding one.
A chemical engineer wished to accumulate a total of interest, determine the present worth of P20000 which is Determine the amount in the fund after the sixth
P50,000.00 in a savings account at the end of 10 years. If due at the end of 9 months. deposit.
the bank pays only 5% compounded quarterly, what a. P16 834.18 a. P13 000
should be the initial deposit? b. P14 648.13 b. P12 000
a. 41,778.60 c. P12 628.34 c. P14 000
b. 20,420.45 d. P18 348.62 d. P15 000
c. 52,411.47 SITUATION 4: PROBLEM 30:
d. 30,420.67 The officers and board of directors of the Philippine A man wishes to bequeath to his daughter P20000 ten
PROBLEM 21: Institute of Civil Engineers desire to award a P3600 years from now. What amount should he invest now if it
If P25000 is invested at 8% interest compounded scholarship annually to deserving civil engineering will earn interest of 8% compounded annually during the
quarterly, how many years will it take for this amount to students for as long as its scholarship fund shall last. The first 5 years and 12% compounded quarterly during the
accumulate to P45 000? fund was started July 1, 1987 by a donor in the amount next 5 years?
a. 7.5 years of P18000. The PICE invested this amount at that time at a. P7 653.65
b. 4.7 years 8% per annum and plans on adding P600 each year to b. P3 573.35
c. 5.8 years the fund from its dues starting July 1, 1988 for as long as c. P7 536.45
d. 6.3 years awards are made. d. P6 357.54
PROBLEM 31: PROBLEM 35: five more years, you withdraw the balance in the fund.
A business man needs P50000 for his operations. One How long will it take money to triple itself if invested at How much was withdrawn?
financial institution is willing to lend him the money for 8% compounded annually? a. P1 320 255
one year at 12.5% interest per annum (discounted). a. 18 years b. P1 508 305
Another lender is charging 14% with the principal and b. 17 years c. P1 084 361
interest payable at the end of one year. A third financier c. 14 years d. P1 406 023
is willing to lend him P50000 payable in 12 equal d. 15 years PROBLEM 40:
monthly installments of P4600. Which is the best offer? PROBLEM 36: Find the nominal rate compounded monthly which is
a. 1st offer What payment X 10 years from now is equivalent to a equivalent to 12% compounded quarterly. What is the
b. 2nd offer payment of Php 1000 six years from now, if interest is corresponding effective rate?
c. 3rd offer 15% compounded monthly? a. 9.58%
d. none a. P 1815.35 b. 10.45%
PROBLEM 32: b. P 1234.65 c. 13.15%
Find the least number of years required to double a c. P 2785.32 d. 12.55%
certain amount of money at 5%. d. P 1678.25 PROBLEM 41:
a. 12 years PROBLEM 37: How many years are required for P1000 to increase to
b. 14 years A man borrows P6400 from a loan association. In P2000 if invested at 9% per year compounded daily?
c. 18 years repaying this debt he has to pay P400 at the end of every a. 8.5 years
d. 10 years 3 months on the principal and a simple interest of 16% b. 7.7 years
SITUATION 5: on the principal outstanding at that time. Determine the c. 4.8 years
On the day his son was born, a man deposited to a trust total amount he has paid after paying his debt. d. 6.3 years
company a sufficient amount of money so that the boy a. P6 856 PROBLEM 42:
could receive annual payments of P10 000 each for his b. P8 576 At a certain interest rate compounded quarterly P1000
college tuition fees, starting with his 18th birthday. c. P9 890 will amount to P4500 in 15 years. What is the amount at
Interest at the rate of 12% per annum was to be paid on d. P7 850 the end of 10 years?
all amounts on deposit. There was also a provision that PROBLEM 38: a. P3 300.12
the grandson could elect to withdraw no annual A chemical engineer wished to accumulate a total of Php b. P2 725.17
payments and receive a single lump amount on his 25th 10 000 in a saving account at the end of 10 years. If the c. P4 090.36
birthday. The son chose this option. bank pays only 4% compounded quarterly, what should d. P2 250.26
33. How much did the boy receive as the single be the initial deposit? PROBLEM 43:
payment? a. P4603.83 If the sum of P12 000 is deposited in an account earning
a. P76 300 b. P6 716.53 interest at the rate of 9% compounded quarterly, what
b. P89 250 c. P7600.78 will it become at the end of 8 years?
c. P70 078 d. P5 448.36 a. P24 457.24
d. P81 000 PROBLEM 39: b. P25 757.42
34. How much did the father deposit? Today, you invest P100 000 into a fund that pays 25% c. P27 424.57
a. P6 300 interest compounded annually. Three years later, you d. P22 577.75
b. P4 520 borrow P50 000 from a bank at 20% annual interest and
c. P4 890 invested in the fund. Two years later, you withdraw
d. P5 250 enough money from the fund to repay the bank loan and
all interest due on it. Three years from this withdrawal
you start taking P20000 per year out of the fund. After
PROBLEM 44: PROBLEM 48:
The time for an investment of $3000 to reach a value of If P10 000 is deposited each year for 9 years, how much
“A” dollars when it is compounded continuously at 8% annuity can a person get annually from the bank every
annual interest is given by: What will the investment be year for 8 years starting 1 year after the 9th deposit is
worth in 10 years? made. Cost of money is 14%.
a. 5777.112 a. P36 345
b. 5003.521 b. P54 850
c. 3555.3 c. P34 675
d. 6676.623 d. P40 200
PROBLEM 45: PROBLEM 49:
Calculate the effective interest rate per month for an A debt of P40 000 whose interest rate is 15%
interest rate of 14% in continuously compounded compounded semi-annually, is to be discharged by a
account? series of 10 semi-annual payments, the first payment to
a. 1.488% be made 6 months after consummation of the loan. The
b. 1.258% first 6 payments will be P6000 each, while the remaining
c. 1.671% 4 payments will be equal and of such amount that the
d. 1.174% final payment will liquidate the debt. What is the amount
PROBLEM 46: of the last 4 payments?
Determine the exact simple interest on Php 500 for the
period from January 10 to October 28, 1992 at 16% a. P5 454
interest. b. P5 850
a. P63.83 c. P4 500
b. P72.51 d. P3 480
c. P60.78 PROBLEM 50:
d. P48.36 What amount of money invested today at 15% interest
PROBLEM 47: can provide the following scholarships: P30 000 at the
By the conditions of a will, the sum of P25000 is left to a end of each year for 6 years; P40 000 for the next 6 years
girl to be held in trust by her guardian until it amounts to and P50 000 thereafter?
P45000. When will the girl receive the money if the fund
is invested at 8% compounded quarterly? a. P214 727
a. 8.39 years b. P198 255
b. 7.42 years c. P241 277
c. 6.52 years d. P254 000
d. 10.23 years