Additional mathematics project work 2007 form 5?

Question:Additional mathematics project work 2007 form 5?

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 first month and this commission 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 of the previous month.

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

1(a)how much does each of them receive
at the end of the 1st year?(2 or
more methods are required for this
question)
(b)what is the percentage change in
their total income for the 2nd year
compared to the 1st year?comment on
the answers.
(c)Ang, Bakar and Chandran, each
decided to open a fixed deposit
account of RM10000 for 3 years
without any withdrawal.

-Ang keeps the amount at an
interest rate of 2.5% per annum
for duration of 1 month renewable
at the end of each month.

-Bakar keeps the amount at an
interest rate 3% per annum for
duration of 3 months renewable at
the end of every 3 months.

-Chandran keeps the amount at an
interest rate of 3.5% per annum
for a duration of 6 months
renewable at the end of every 6
months.

(i) Find the total amount each of them
will receive after three years.

(ii) Compare and comment on the
different in the interests
received. If you were to invest
RM10000 for the same period of
time, which fixed deposit account
would you prefer? Give your
reasons.

FURTHER EXPLORATION

2(a)When Chandran's first child, Johan is born, Chandran invested RM300 for him at 8% compound interest per annum. He continues to invest RM300 on each of Johan's birthday, up to and including his 18th birthday?

(b)If Chandran starts his investment with RM500 instead of RM300 at the same interest rate, calculate on which birthday will the total investment be more than RM25000 for the first time.



Answers:
g
THE ANSWERS:

Q1.

In the n the month:

Bakar earns 1000 + 100(n - 1).

His pay is increasing in arithmetic progression, with a starting value of 1000 and a common difference of 100.

Chandran makes 100 * 1.5^ (n - 1).

His pay is increasing in geometric progression, with a starting value of 100 and a common ratio of 1.5.



a)

At the end of the first year, Chandran has:

6(2*1000 + 11*100)

= 6 * 3100

= 18600 RM.

That's using the formula for the sum of an arithmetic series. You can also find the average monthly pay and multiply that by 6. It's not really different though.



Chandran has 100(1.5^12 - 1) / (1.5 - 1)

= 25749.27 RM.

That's using the formula for the sum of a geometric series.

I don't know any alternative technique for doing this, unless you are going to calculate from first principles, as you do when proving the formula.



Ang earns 2000 * 12 = 24000 RM. If you want another method, add up 12 lots of 2000, but what's the difference?



b)

Work out the income of each for the second year, taking into account the increased salary for Ang, and the changes in the starting pay and common difference for Chadran. Presumably Bakar continues in the same manner as before.

When you have the incomes worked out for the second year, you can find the percentage increase.



c)

i) RM10778.00

RM10938.07

RM11097.02



ii) The 3.5% is going to give you a higher interest... the difference in the compounding periods is negated by the fact that each different compounding period has a higher interest rate than the previous. Had all been the same interest rate the monthly one would have given you a slightly larger return. For instance all been 2.5% per annum... the quarterly (every three months) would have yielded only 776.33



None of them... they don't pay enough... I would invest the money in stocks...



Q2.

a)

RM 300-8% per annum for 18yrs

1st year- 300(8/100) =24

Hence RM300+RM24=RM324

2nd year- 324(8/100) =25.92

Hence RM324+RM25.92=RM349.92



*this continues until the 18th year-RM1198.79 (ans)



b)

RM500- 8% per annum-total investment will be more than RM25000 for the first time



Use the same technique above in Q2 (a) to apply on this question..

The answer will be 50years 11months-RM25171.42

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