A few days ago
cat s

# project SPM 2007 for additional mathemtics?

Ang, Bakar and Chandran are friends and they have just graduated from a local university. Ang works in a company with a starting pay of RM2000 per month. Bakar is a sales executive whose income depends solely on the commission he receives. He earns a commission of RM1000 for the 1st month increases by RM100 for each subsequent month. On the other hand, Chandran decides to go into business. He opens a cafe and makes a profit of RM100 in the first month. For the first year, his profit in each subsequent month is 50% more than that of the previous month.

In the second year, Ang receives a 10% increment in his monthly pay. On the other hand, the commission received by Bakar is reduced by RM50 for each subsequent month. In addition, the profit made by Chandran is reduced by 10% for each subsequent month.

1)What is the percentage change in their total income for the 2nd year compared to the 1st year? Comment on the answers.

2)tota lthey will receive in 1st year?

A few days ago
Michael

Let’s do each person separately and then add:

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.

0