GEST 1001 – QUANTITATIVE REASONING FOR BUSINESS

ASSIGNMENT TWO

Section A

Solve the following multiple-choice questions and write your answers on the Answer Table provided at the bottom of this page.

1.   An effective annual rate of            corresponds to a nominal interest rate of 12% p.a. compounded quarterly.

A. 12%                      B. 12.16%               C. 12.35%                        D. 12.55%

2.   Textbook p.255, question 10: Find the amount that must be invested ……

A. $14, 174.71           B. $9,032.70           C. $11778.13           D. $18,000

3.   A university graduate with  x   years of education can expect to receive an average annual salary of

y   dollars per year, where  y = 100x 2/3  + 5200 ,  4 ≤ x ≤16 .    For what value of  x   is the average

annual salary increasing at the rate of $450 per year of education?

A.  4 years                 B. 9 years                C. 12 years              D. 16 years

4.   Textbook p.546, question 58: The position function … (correct your answer to the nearest second)

A.  8 seconds             B. 7 seconds            C. 5 seconds            D. 0 second

5.   Find the equation of the line that is tangent to the graph of the function  y = (x2  +1)(1 - x3 ) at the point (1, 0).

A.  y = −6x                                                   B.  y = 6x + 1

C.  y  = −6(x − 1)                              D.  y  = −3x2 (x2  + 1) + 2x(1 − x3)

6.   Textbook p.249, question 14: (Assuming interest is compounded monthly) Find the monthly periodical payment … (correct your answer to two decimal places)

A. $49.49                  B. $51.43                 C. $50                     D. $53.33

Section B

Solve the following problems carefully with detailed workings, steps and answer statements. Write all your answers on the spaces provided below each question.

7.   A factory must replace her machinery two years from nowata cost of $100,000.    The manager has to set aside equal amounts of deposits at the beginning of each quarter to settle the payments. Ifthe interest is 5.5% p.a. compounded quarterly, solve the following problems.     (Round all the answers to two decimal places.)

(a) What is the size of the equal quarterly deposits? (10%)

(b) What is the total amount that the factory paid for the machinery? (5%)

(c) If the manager decides to deposit a certain amount (lump-sum) of money at the beginning of the first quarter instead of setting aside equal deposit at each quarter, what is the size of this certain amount?    (5%)

8.   Mr. Chan has to pay for a loan with equal payments of $1500 at the beginning of each month for 25

years. If the interest rate is 11.5% p.a. compounded monthly, calculate: (a)    the total amount repaid, (5%)

(b)    the present value of the loan (correct to 2 decimal places),     (10%)

(c)    the total amount of interest paid (correct to 2 decimal places).     (5%)

Section C

The  following  questions  are  for  your  self-practice,  no  submission  is necessary.

9.      For a monopolist’s product, the demand function is   p = q+10/q+100 where p is the unit price in dollars, q is the

quantity demand in units, and the cost function is   C(q) = 2q + 5  dollars. (a) Find the marginal revenue function.

(b) Use differentiation to approximate the revenue earned by selling the 11th unit.

(c) Determine the price & production level for which the profit is maximized.

10.     To complete your last year in the secondary school and then go through the university, you will need $10,000 per year for 4 years, starting next year (that is, you will need to withdraw $10,000 one year from today).   Your rich uncle offers to put you through school, and he will deposit a sum of money in a bank paying interest of 8% p.a. compounded annually and that sum is sufficient to provide the four payments of $10,000 each.   His deposit will be made today.

(a)   How large must the deposit be?

(b)   How much will be in the account immediately after you make the first withdrawal?

(c)   How much will be in the account at the end of year 4 if you do not withdraw within these 4 years?

11.     For a certain population, if  E is the number of years of a person’s education and   S   represents average annual salary in dollars, then for   E ≥ 7 ,

S = 340E2  - 4360E + 42800

(a)  How fast is the salary changing with respect to education when   E = 16 ?

(b)  At what level of education does the rate of change of salary equal $5000 per year of education?

12.      To what sum will $2000 amount in eight years if invested at a 6% effective rate for the first four years and at 6% compounded semiannually thereafter?

13.     If the rate of inflation for certain goods is   7 4/1 % compounded daily, how many years will it take for the average

price of such goods to double? (Assume there are 365 days in a year.)

14.     In 10 years, a $40,000 machine will have a salvage value of $4000.A new machine at that time is expected to sell for $52,000. In order to provide funds for the difference between the replacement cost and the salvage value, a sinking fund is set up into which equal payments are placed at the end of each year. If the fund earns 7% compounded annually, how much should each payment be?

(Note: A sinking fund is a fund into which periodic payments are made in order to satisfy a future obligation.)