Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2020 | Feb-Mar | (P1-9709/12) | Q#8

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Question

A woman’s basic salary for her first year with a particular company is $30000 and at  the end of the year she also gets a bonus of $600.

a)For her first year, express her bonus as a percentage of her basic salary.

At the end of each complete year, the woman’s basic salary will increase by 3% and  her bonus will increase by $100.

b)Express the bonus she will be paid at the end of her 24th year as a percentage of  the basic salary paid during that year.

Solution

From the given information, we can collect following information.

The basic salary for her first year;

The bonus at the end of first year;

a)

Her bonus as percentage of her salary;

Her bonus is 2% of her first year’s salary.

 

b)

Salary of 1st year;

Since annual rate of growth continues to be constant at 3%.

Salary of 2nd year;

Similarly, salary of 3rd year will be;

Hence, salary for 4th year will be;

It is evident that this model represents Geometric Progression (G.P).

Now, we find her salary on 24th year.

Expression for the general term  in the Geometric Progression (G.P) is:

Therefore;

We can find the common ratio as follows.

Expression for Common Ratio () in a Geometric Progression (G.P) is;

Hence;

Hence;

Her bonus on 24th year will be;

Finally, we can express this bonus as percentage of 24th year’s salary;

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