[ INTRODUCTION TO MATHS]
COURSE CODE: CSC102
Name: Syed Shujaat Hussain Zaidi
Student ID: 52239
Program: BBA-H
Final Exam
[To Sir Abdul Khaliq &
Sir Hamid Saeed Khan]
Question Number 1: [CLO3, PLO4]
marks]
[2.5+2.5+2.5+2.5 = 10
Nintendo, a leading manufacturer of video games is about to introduce four new games. The
accompanying table summarizes price and cost data. Combined fixed costs equal $500,000.
Game-1
Game-2
Game-3
Game-4
Selling price
$50
$45
$30
$20
Variable cost per unit
$20
$15
$10
$10
0
a)
b)
c)
d)
Determine a joint total revenue function for sales of the video games.
Determine a joint total cost function for development of the video games.
Determine the profit function for sales of the video games.
What is profit if the firm sells 8000, 10000, 20000 and 5000 units respectively of the
four video games.
Answer Number 1:
(See image below for answer)
Question Number 2: [CLO5, PLO3]
[1+3+3+3 = 10
marks]
A. A $10,000 certificate of deposit earns simple interest of 8 percent per year. Calculate the
total earned money over the 5year period?
Answer Number 2-A: Calculation of the total earned money over the 5year period
Deposit Amount = $ 10,000
Rate of interest = 8% per year.
Term = 5 years
Interest earned = PTR/100
Where p = Principal,
T = Time,
R = Rate of interest
Interest earned over the 5year period = ($ 10,000*5*8)/100
=$ 4000
Total amount = Principal + Interest = $ 10,000+ $ 4000 = $ 14000
B. A sum of $22,000 is invested in a savings account which pays interest at the rate of 7
percent per year compounded quarterly. If the amount is kept on deposit for 10 years, what
will the compound amount equal? How much interest will be earned during the 10Years?
Answer Number 2-B: Deposit Amount = $ 22000
Rate of interest = 7% Compounded Quarterly
Deposit term = 10 years
We know that Future value = Present value (1+i/4) ^4n
Where n = No. of years,
I = Rate of interest
Future value = $ 22000 (1 +7/400) ^4*10
= $ 22000 (1.0175) ^40
= $ 22000*2.001597
= $ 44035.13
Hence the Compounded Amount is $ 44035.13
Effective interest rate = [ (1+i/m) ^m - 1] *100
Here m = Compounding Frequency per year i.e., 4 times
= [ (1+7/400) ^4 - 1] *100
= [1.0175^4 - 1] *100
= 0.071859
= 7.1859%
Effective Annual interest rate is 7.1859%
C. A Company wants to deposit $1,000,000 per year in an investment which earns interest of
10 percent per year. Assume the first deposit is made at the end of the current year and
additional deposits at the end of each following year.
a) To what sum will the investment grow at the time of the 10th deposit?
b) How much interest will be earned?
Answer Number 2-C:
C)
Year
Opening Balance
1
Interest @ 10% Total amount Amount Deposited
$1,000,000
$1,000,000
Closing Balance
2
$1,000,000
$100,000.0
$1,100,000.0
$1,000,000
$2,100,000.0
3
$2,100,000.0
$210,000.0
$2,310,000.0
$1,000,000
$3,310,000.0
4
$3,310,000.0
$331,000.0
$3,641,000.0
$1,000,000
$4,641,000.0
5
$4,641,000.0
$464,100.0
$5,105,100.0
$1,000,000
$6,105,100.0
6
$6,105,100.0
$610,510.0
$6,715,610.0
$1,000,000
$7,715,610.0
7
$7,715,610.0
$771,561.0
$8,487,171.0
$1,000,000
$9,487,171.0
8
$9,487,171.0
$948,717.1
$10,435,888.1 $1,000,000
$11,435,888.1
9
$11,435,888.1
$1,143,588.8
$12,579,476.9 $1,000,000
$13,579,476.9
10
$13,579,476.9
$1,357,947.7
$14,937,424.6 $1,000,000
$15,937,424.6
Total $5,937,424.6
a So the investment amount will become to $ 159,37424.6
b Interest earned = $ 59,37424.6
D. A person wants to generate four installments of $1,000 in the following four years. How
much money should be invested, if the interest rate is 10 percent per year.
Answer Number 2-D: Calculation of Present value of an Annuity
Annuity * PVAF = Present value
$ 1000* PVAF (10%, 4) = Present value
Present value = $ 1000*3.169865
Present value = $ 3169.865.
Question Number 3: [CLO4, PLO3]
[5+5 = 10
marks]
A. Apply the Inverse Matrix method (AX=B method) to find the unique solution of below
mentioned system of multivariable equations.
2𝑥 + 3𝑦 = 18
6𝑥 + 3𝑦 = 30
Solution:
(See image below for answer)
B. Apply Crammer’s Rule to find the solution of below mentioned system of multivariable
equations.
𝑥+𝑦+𝑧 = 6
2𝑥 − 𝑦 + 3𝑧 = 4
4𝑥 + 5𝑦 − 10𝑧 = 13
Solution:
(See image below for answer)
Question Number 4: [CLO2, PLO1]
[4+3+3 = 10
marks]
A. Determine the concavity of the parabola representing the quadratic function, its yintercept, its x-intercepts and the coordinates of the vertex. Also sketch the Parabola.
𝑓(𝑥) = 10𝑥 2 − 70𝑥 + 100
Solution # 4-A:
(See image below for solution)
B. The demand function for a product is
𝑄 = 𝑓(𝑝) = 𝑝2 − 90𝑝 + 2025
; 0 ≤ 𝑝 ≤ 45
Where Q equals the number of units demanded and p equals the price per unit, stated in
dollars.
a) What type of function is this?
b) How many units will be demanded at a price of $30?
c) What price would result in zero demand for the product?
Solution # 4-B:
(See image below for solution)
C. Find the Distance, Slope and Midpoint of the line segment connecting (5,-10) and (15,-20).
Also find the equation of this line.