A woman’s basic salary for her first year with a particular company is $30,000 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
(a) The bonus for the first year is $600. The basic salary is $30,000. To find the bonus as a percentage of the basic salary:
\(\text{Percentage} = \left( \frac{600}{30000} \right) \times 100 = 2\%\)
(b) The bonus at the end of the 24th year is calculated as follows:
\(Initial bonus = $600\)
\(Increase over 23 years = 23 \times $100 = $2300\)
\(Total bonus = $600 + $2300 = $2900\)
The basic salary at the end of the 24th year is:
\(\text{Salary} = 30000 \times 1.03^{23} \approx 59207.60\)
Express the bonus as a percentage of the salary:
\(\text{Percentage} = \left( \frac{2900}{59207.60} \right) \times 100 \approx 4.9\%\)
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