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WELCOME TO THIS PAGE INTENDED FOR STUDENTS AT THE UNIVERSITY OF THE WESTERN CAPE REGISTERED IN 2010  FOR THE MODULE:

QSF  132

SALARY NOTCHES

QUESTION 1 (From QSF June 2008 paper)

In 2007 it was proposed by the South African educational authorities that teachers’ salaries would range from R115 000 to R459 000 per annum. The salary range was divided into 74 notches, with R115 000 being the 1st notch and R459 000 being the 74th or last notch.

1.1       Express the ratio of R115 000 to R459 000 in its simplest form;

1.2       By what percentage is R459 000 more than R115 000? (Give your answer to the        nearest percentage.)

1.3       If the difference between any two consecutive notches is a constant, determine   that constant difference.

1.4       Is the percentage increase from one notch to the next consecutive notch also a   constant?  Motivate your answer by calculating the percentage increase from the       1st  notch to the 2nd , and that from the second last to the last notch.       (7)

QUESTION 2

In 2009 it determined by the South African educational authorities that salaries would range from R62 418 to R542 271 per annum. The salary range was divided into 221 notches, with R62 418 being the 1st notch and R542 271 being the 221st or last notch.

2.1       Express the ratio of R62 418 to R542 271 in its simplest form;

2.2     By what percentage is R542 271  more than R62 418? (Give your answer to the nearest percentage

2.3     If the percentage increase from one notch to the next is a constant of 1%,      calculate the second notch, the second last notch etc.

2.4     Do you agree that with the assumption of a 1% increase from one notch to the

next?

2.5     Use the formula:

where r = 1.01, in order to answer question 2.4 (if you have not done so already).

2.6     In 2010 it was agreed that all salary notches would be adjusted by 7.5% upwards.  Calculate the new first and the last notches.

2.7     In terms of the 2010 agreement, do the salaries relevant to   consecutive notches still differ by the ratio of 1%?

QUESTION 3

Use the formula ,

together with the number of notches = 221, first term = R62 418 and last term = R542 271, and prove by means of logarithms that   r =  1.01.

SOLUTION:

If

then

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