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

To solve the questions, let's go step by step.

1(a) To calculate how much each of them receives at the end of the first year, we need to consider their individual incomes and profits each month.

For Ang:
Starting pay per month: RM2000
Increment in the second year: 10% of RM2000 = RM200

At the end of the first year, Ang's total income:
First-year income: RM2000 * 12 = RM24,000
Second-year income: (RM2000 + RM200) * 12 = RM25,200

Ang's total income at the end of the first year = RM24,000 + RM25,200 = RM49,200

For Bakar:
Commission for the first month: RM1000
Increment in commission for each subsequent month: RM100

At the end of the first year, Bakar's total income:
First-month commission: RM1000
Second-month commission: RM1000 + RM100 = RM1100
...
Twelfth-month commission: RM1000 + RM100 * (12 - 1) = RM2100

Sum of commissions from the first year:
RM1000 + RM1100 + ... + RM2100

Using the formula for the sum of an arithmetic series:
Sum = (Number of terms / 2) * (First term + Last term)

Number of terms = 12 (months)
First term = RM1000
Last term = RM2100

Sum = (12 / 2) * (RM1000 + RM2100) = 6 * RM3100 = RM18,600

Bakar's total income at the end of the first year = RM18,600

For Chandran:
Profit in the first month: RM100
Profit in each subsequent month: 50% more than the previous month

At the end of the first year, Chandran's total income:
Sum of profits from the first year:
RM100 + (RM100 * 1.5) + (RM100 * 1.5^2) + ... + (RM100 * 1.5^11)

Using the formula for the sum of a geometric series:
Sum = First term * (1 - Common ratio^n) / (1 - Common ratio)

First term = RM100
Common ratio = 1.5
Number of terms = 12 (months)

Sum = RM100 * (1 - 1.5^12) / (1 - 1.5) = RM100 * (1 - 1.5^12) / (-0.5) = RM100 * (1 - 1.5^12) / 0.5
You can calculate the exact value using a calculator.

Chandran's total income at the end of the first year = the calculated sum

1(b) To find the percentage change in total income for the second year compared to the first year, use the formula:
Percentage change = ((New value - Old value) / Old value) * 100

New value = Total income for the second year
Old value = Total income for the first year

Calculate the percentage change for each individual and comment on the results.

1(c) To find the total amount each of them will receive after three years from the fixed deposit accounts, consider their respective interest rates and durations.

(i) Using the given interest rates and durations, calculate the total amount for each person after three years.

For Ang:
Interest rate = 2.5%
Duration = 1 month renewed at the end of each month

You can use the compound interest formula to calculate the total amount. Plug in the values and calculate.

For Bakar:
Interest rate = 3%
Duration = 3 months renewed at the end of every 3 months

Again, use the compound interest formula to calculate the total amount.

For Chandran:
Interest rate = 3.5%
Duration = 6 months renewed at the end of every 6 months

Apply the compound interest formula to calculate the total amount.

(ii) Compare the differences in the interests received by each person. Calculate the differences and comment on them. Determine which fixed deposit account would be preferred if investing RM10000 for the same period of time. Consider the amounts received and the reasons behind the preference.

FURTHER EXPLORATION

2(a) To calculate the total investment when Chandran invests RM300 for Johan at 8% compound interest per annum, use the compound interest formula. Repeat this calculation for each of Johan's birthdays up to and including his 18th birthday. Keep adding the investments on each birthday to find the total investment.

2(b) To determine on which birthday the total investment will be more than RM25000, repeat the same calculation as in 2(a) but with an initial investment of RM500 instead of RM300. Identify the birthday when the total investment exceeds RM25000 for the first time.