Mr Lee and his wife are going for a family trip to Thailand. The table shows the travel insurance premiums payable for individual and family coverage.

(a)
If Mr Lee's family trip last for $n$ days, find the possible values of $n$ if the total travel insurance premium for Mr Lee's family is cheaper for individual policy than the family policy.

Answer n = ...
(b)
Before Mr Lee travelled, he exchanged a total of Singapore dollars (SGD) $1000 at a money changer in Singapore. The exchange rate was shown below.

Unit Currency Sell Buy
100 Thai baht 4.2194 3.5002

During the trip, they spent a total of 19836 Thai baht.

Mr Lee exchanged their remaining Thai baht to SGD from the same money changer when he returned back to Singapore. Calculate the amount of money he received in SGD.

Answer SGD $ ...

Unit	Currency	Sell	Buy
100	Thai baht	4.2194	3.5002

(c)

The personal income tax is a tax levied on the annual chargeable income of working adults by the government. In Singapore, the personal income tax rates for resident taxpayers are progressive, thus the higher the chargeable income, the higher is the tax rate and the more one will need to pay. The table below shows part of the income tax rates in Singapore.

Chargeable income	Income tax rate (%)	Gross tax payable ($)
First $20 000	0	0
Next $10 000	2	200
First $30 000	-	200
Next $10 000	3.5	350
First $40 000	-	550
Next $40 000	7	2 800
First $80 000	-	3 350
Next $40 000	11.5	4 600
First $120 000	-	7 950
Next $40 000	15	6 000
First $160 000	-	13 950
Next $40 000	18	7 200
First $200 000	-	21 150
Next $40 000	19	7 600

Mr Lee is married and stays with both his parents.

Given that chargeable income refers to gross annual income less tax deductions, calculate his gross annual income if his income tax payable is $9567.

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Worked solution

3(a)

1. Compare the costs if the trip is within the first 3 days.

For $n\leqslant 3$ ,

Individual policy for Mr Lee and his wife:
$2(\$34)=\$68$

Family policy has a $20\%$ discount:
$\$75\times 80\%=\$60$

Since $\char36{}68>\char36{}60$ , the individual policy is not cheaper for $n\leqslant 3$ .

2. Form expressions for the costs when the trip is more than 3 days.

For $n>3$ ,

Individual policy for two adults:
$2\left[34+8(n-3)\right]$
$=2(8n+10)=16n+20$

Family policy:
$75+15(n-3)$
$=15n+30$

3. Set up and solve the inequality for individual policy to be cheaper.

Individual policy is cheaper than family policy:
$16n+20<15n+30$
$n<10$

4. Combine with the condition for this case and state integer possible values of $n$.

This case is for $n>3$ , and we found $n<10$ .

Since $n$ is the number of days, $n$ is a positive integer.

Therefore,
$3<n<10$

So the possible values are
$n=4,5,6,7,8,9.$

Answer

$n=4,5,6,7,8,9$ days

3(b)

1. Calculate the amount of Thai baht received for SGD \$1000 using the sell rate.

Since the money changer sells Thai baht at $4.2194 for 100 Thai baht,
$\text{Thai baht received}=\frac{1000}{4.2194}\times 100=23700.052\ldots$

2. Find the remaining Thai baht after spending 19836 Thai baht.

$\text{Remaining Thai baht}=23700.052\ldots-19836=3864.052\ldots$

3. Convert the remaining Thai baht back to SGD using the buy rate.

Since the money changer buys Thai baht at $3.5002 for 100 Thai baht,
$\text{SGD received}=\frac{3864.052\ldots}{100}\times 3.5002$
$=135.249\ldots$
$\approx 135.25$

Answer

SGD $135.25

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Mr Lee and his wife are going for a family trip to Thailand. The table shows the travel insurance premiums payable for individual and family coverage.

Worked solution

3(a)

3(b)

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