Mrs Ang runs a small tuition centre for secondary school students. The tables provide information on the cost of running the centre. The centre is closed on Monday and Tuesday.

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.