Question

Sivamani is attending an interview for a job and the company gave two offers to him. Offer A: Rs 20,000 to start with followed by a guaranteed annual increase of 6% for the first 5 years. 

Offer B: Rs 22,000 to start with followed by a guaranteed annual increase of 3% for the first 5 years. 

What is his salary in the 4^th year with respect to the offers A and B?

Answer 1

For A

Starting salary (a) = Rs 20,000 

Annual increase = 6% of 20000 

= 5/100 x 20000 = Rs 1200 

Salary for the 2^nd year = Rs (20000 + 1200)

= Rs 21200 

Here a = 20,000; r = 21200/20000 = 212/200 = 106/100 = 53/50

n = 4 years 

t_n = ar^{n - 1}

Salary at the end of 4^th year = 23820

For B 

Starting salary = Rs 22000 

(a) = 22000 

Annual increase = 3% of 22000 

= 3/100 x 22000 = Rs 660 

Salary for the 2^nd year = Rs 22000 + Rs 660 

= Rs 22,660

Here a = 22000; r = 22660/22000 

= 2266/2200 = 1133/1100 = 103/100

Salary at the end of 4^th year = 22000 x (103/100)^{4 - 1} 

= 22000 x (103/100)³ 

= 22000 x (103/100) x (103/100) x (103/100) 

= 24039.99 = 24040 4 year Salary for A = ₹ 23820 and 4 year Salary for B = ₹ 24040

= 24039.99 = 24040 

4^th year Salary for A = Rs 23820 and 4^th year Salary for B = Rs 24040