Ang: Year 1: Gets 2000 per month.

Year 2: Gets 2000*(1.1) = 2200 per month

Annually: Year 1 = 2000*12 = 24000

Year 2 = 2200*12 = 26400

Bakar: Year 1: 1000 for month 1, 1000 + 100 for month 2, 1000+100+100 for month 3, etc.

Year 2: He will be making 1000 + 100(12) = 2200 at the beginning of year 2. So in year 2 he will make 2200 + 2200 – 50 + 2200 – 50-50, etc.

Annually: Year 1 (1000)+(1000 + 100) + (1000+100+100) + … + 1000 + 11*100

= 1000*12 + 100+200+…+1100

=12000 + 100 * (11*12)/2

=12000 + 50*132

=12000 + 6600

=18600

Year 2 – 2200 + 2200 – 50 + 2200 – 100 + … + 2200 – 50*11

= 2200*12 – (50+100+150+…+550)

=26400 – 50*(1+2+…+11)

=26400 – 50*(11*12)/2

=26400 – 25*132

=26400 – 3300

=23100

Chandran: Year 1: 100 in month 1, 100*1.5 in month 2 100*1.5*1.5 in month 3, etc.

Year 2: At the beginning of year 2, he will make 100*1.5^12 = X. So in year two he will make X + X(1-.1)+X(1-.1)(1-.1), etc.

Annually:

Year 1: 100 + 100*1.5 + 100*1.5^2+…+100*1.5^11

=100(1+1.5+1.5^2+1.5^11)

=100*(1-1.5^12)/(1-1.5)

=25,749

Year 2: X + .9X + .9^2X + … + .9^11X

=x*(1+.9 + … + .9^11)

=X*(1-.9^12)/(1-.9)

=93,102

Summary: Year 1: 24000+18600+25479 = 68079 (answer to #2)

Year 2:26400+23100+93102 = 142602

#1: 142602/68079 – 1 = 109% – even though their income started to decrease in year 2, their starting income in year 2 was significantly higher than in year 1 and did not decrease as quickly as it had increased in year 1.