A software engineer earns a monthly salary of Rs 30,000 in the first year of employment. At the beginning of each subsequent year, her monthly salary is increased by Rs 2,500. For every year, 10 % of that year’s total earnings (calculated on the annual salary) is deducted as income tax before the amount is paid to her.
(i) Show that the sequence of her annual salaries forms an arithmetic progression and write its first term and common difference.
(ii) Find her annual salary in the 6th year.
(iii) Calculate her total gross earnings (before tax) over the first 6 years.
(iv) After deducting 10 % income tax each year, find the total net amount she actually receives over the 6-year period.