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Q1. Drink Stall (11 marks)

Mike has been selling drinks for the last 10 years. He observed that on hot days, his drink sales were good, however, when the weather gets too hot or too cold, his drink sales suffered.

He collected past data on his drink sales (y) for different average temperature (x) of the day. He obtained the relationship as, y = -2.5(x - 20.5)2 + 3.8x + 1743.

a) Prepare the table of values for different x values from -5 to 45, at increment of 5, and compute the corresponding y

b) Plot the graph Determine the following:

c) The temperature at which the maximum sales will occur

d) The maximum sales number

e) The two temperatures at which there will be no sales at all

Q2. Housing Loan (12 marks)

Michelle is planning to buy a new house which costs $150,000. She has saved some money from her years of hard work, and she plans to use part of her savings to pay for the house, and to loan the rest from the bank. The bank will charge her a yearly interest of 2% for the loan over 10 years. She does not like to loan too much from the bank and she reckons that she will use between $10,000 to $30,000 of her savings to pay for the house.

She is interested to know the earliest month at which the amount she owes the bank (residual loan amount) will be less than $50,000.

Prepare a table of results (Table 1) with the following columns:

a) Amount to use from her savings, from $10,000 to $30,000 at increment of $5,000

b) Bank loan amount

c) Monthly payment to the bank assuming payment occurs at the end of the period

d) Earliest month to reach residual loan of less than $50,000

To determine the result for part d, you will need to prepare a table of calculations that computes the residual loan at the end of each month (Table 2). Table 2 should have at least 2 columns, End of Month and Residual Loan.

e) Extract the result for part d using a suitable Excel function from Table 2, instead of just eye- balling, and fill in the answers in Table 1.

What is the amount of bank loan for the earliest month to reach residual loan of less than $50,000, to be month 76?

f) The minimum amount (in steps of $100)

g) The maximum amount (in steps of $100)

Q3. Investment Analysis (10 marks)

Michael intends to invest in a financial product, where he will invest a fixed amount of $10,000 at the start of each year for 10 years. The fund manager will charge him an up-front fund management fee of 3% for the $10,000 at the start of the year. The newly invested amount (minus the fund management fee) plus whatever balance amount in his investment account will be guaranteed to earn an annual return rate of 2%. For this financial product, Michael is not permitted to terminate pre- maturely, or withdraw any funds from his investment account, until the end of 10 years.

Prepare a table with the following columns:

a) Year from 0 to 10

b) Cumulative amount invested at start of year

c) Investment account balance at start of year

d) Investment account balance at end of year

Ignoring the time value of money, determine if a positive return (that is, the investment account balance exceeds the cumulative amount invested by at least $1) occurs at the start of the year.

e) You can add a new column to indicate Yes/No for Positive return.

f) Determine the year at which the first positive return occurs.

g) What should the return rate be for the first positive return year to occur at the start of year 3?

Using the earlier scenario of an up-front fund management fee of 3% and an annual return rate of 2%,

h) Calculate the Internal Rate of Return (IRR) at the end of 10 years for this investment.

Q4. Ice-cream Shop (12 marks)

Megan wants to run an ice-cream shop and she estimates that the investment she needs will include:

• Purchase of shop furniture and equipment (e.g. tables, chairs, fridge etc.) which will cost her a one-time expense of $4000

• Monthly rental of $1000 due at the start of each month

• Monthly salary for her one and only staff at $1200, payable at the end of each month

She estimates that she can sell 600 scoops of ice-creams in the first month, and expects sales to increase at 5% each month. The cost of acquiring the ice-creams from her supplier is $10 per tub, and each tub can produce 24 scoops. She sells her ice-creams at $3.50 per scoop.

Prepare a table with the following columns:

a) Start of Month, from month 1 to month 15

b) Ice-cream sales, round up to the nearest integer

c) Monthly expenses which will include rental, salary and ice-cream cost (to 2 decimal places)

d) Monthly income from sales of ice-creams (to 2 decimal places)

e) Profit (to 2 decimal places)

f) Cumulative profit (to 2 decimal places) Determine the following:

g) By the end of which month will Megan earn enough profit to cover the $4000 she has spent on the shop furniture and equipment

h) Create a Data Table to tabulate the answer to part g for different sales increment percentage starting from 6% to 12%, at 1% increment

Q5. Flat Purchase (10 marks)

The government of country ABC plans to build public housing flat units for its citizens to apply for purchase. There are three types of flats namely, 3-bedroom, 4-bedroom and 5-bedroom. The number of units, the number of applicants, the average cost per unit, and the average selling price per unit, for the three types are given in the table below.

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