洪太太经营着一家面向中学生的小型补习中心。表格提供了运营该中心的成本信息。该中心在周一和周二关闭。

1. Convert the loan period to years and calculate the simple interest.

Renovation cost borrowed = $40 000

$30$ months $= \dfrac{30}{12}=2.5$ years

Simple interest:

$I = 40000 \times \frac{2}{100} \times 2.5 = 2000$

Interest incurred = $2000

2. Find the equal monthly instalment.

Total amount to repay:

$40000+2000=42000$

Monthly instalment:

$\frac{42000}{30}=1400$

1. Identify the original cost and calculate the 15% discount amount.

Original cost of furniture and IT equipment $= \char36{}5100$

Saving $= 15\% \times 5100$

$= \dfrac{15}{100}\times 5100$

$= 765$

1. State a clear assumption about class size and calculate the monthly fee income.

Assume each class has the minimum of 5 students.

Lower Secondary classes per week: $6+6=12$

Upper Secondary classes per week: $6+8=14$

Monthly income from Lower Secondary:
$12\times 5\times \$200=\$12\,000$

Monthly income from Upper Secondary:
$14\times 5\times \$300=\$21\,000$

Total monthly income:
$\$12\,000+\$21\,000=\$33\,000$

2. Calculate the monthly running costs of the tuition centre.

Rental per month: $\char36{}8000$

Printing and stationery per month:
$4\times \$100=\$400$

Administrative staff cost per month: $\char36{}1800$

Teaching cost for weekday classes:
$12\times 2\times 4\times \$70=\$6720$

Teaching cost for weekend classes:
$14\times 2\times 4\times \$90=\$10\,080$

Cleaning cost per month:

The centre is closed on Monday and Tuesday, so it opens $5$ days per week.
$5\times 4\times \$45=\$900$

Total monthly running cost:
$\$8000+\$400+\$1800+\$6720+\$10\,080+\$900=\$27\,900$

3. Find the monthly profit and check the monthly profit target after 6 months.

Monthly profit:
$\$33\,000-\$27\,900=\$5100$

Since
$\$5100\geq \$5000,$
Mrs Ang would meet the target of making a profit of at least $\char36{}5000$ per month thereafter, under this assumption.

4. Calculate the start-up cost plus interest incurred.

From part (b), saving on furniture and IT equipment is $\char36{}765$.

Actual cost of furniture and IT equipment:
$\$5100-\$765=\$4335$

Interest incurred from part (a):
$30\times \$1400-\$40\,000=\$42\,000-\$40\,000=\$2000$

Start-up cost plus interest:
$\$40\,000+\$4335+\$2000=\$46\,335$

5. Compare 6-month profit with the amount to be recovered and make a justified decision.

Profit in 6 months:
$6\times \$5100=\$30\,600$

Compare with start-up cost plus interest:
$\$30\,600<\$46\,335$

Therefore, Mrs Ang will not recover her start-up cost and interest within 6 months under the assumption of 5 students per class.