① You shouldn't be adding S$252.761 to the S$4631.616.

That S$252.761 was calculated using the higher exchange rate of 1.8723. That was converting pounds to its equivalent in Singapore Dollars (S$) when Ricky was BUYING pounds (£)

This means that he had to pay S$252.61 to obtain £135.

When exchanging it back to Singapore Dollars, he is SELLING his pounds.

The exchange rate is lower at 1.8267.

(And that is how money changers and banks earn a profit. Selling to customers at a more expensive rate than buying from customers)


So if you want to use this method of converting the £135 back to S$ , (i.e as good as RICKY is getting a refund for the wallet (in pounds) and then exchanging the pounds back to Singapore Dollars)

S$(135 × 1.8267) ≈ S$246.61 (nearest cent)

He would get back less than what he had to pay for in the first place.


S$246.61 + S$4631.62(rounded to nearest cent)
= S$4878.23

Percentage loss

= (5000 - 4878.23) / 5000 × 100%

= 2.4354%
≈ 2.44% (3s.f)

② Not advisable to use this method as it is not known if the person spent on anything else during the trip.

This method is assuming that he didn't spend on anything (since you've added back the money for the wallet)

Furthermore, we could actually have saved time on all those calculations and also avoid all those truncation errors : (see why below)




③ With regards to profit and loss concept, this is how we can think about it :

For every Pound you want to buy, you have to pay 1.8723 Singapore Dollars.

But when you try to exchange this Pound back to Singapore Dollars (i.e selling your pounds away) you only get 1.8267 Singapore Dollars back

The percentage loss you make for every 1 Pound that was not used and exchanged back is :


(1.8723 - 1.8267)/1.8723 × 100%

= 0.0456/1.8723 × 100
≈ 2.4355%
= 2.44% (3s.f)


No matter how many pounds you have left unspent and exchanged back, this percentage never changes.



Why so?


Let's say you had x pounds left (£x), where x can be any amount.

Amount in S$ you had to pay/exchange to get this x pounds in the first place

= S$(1.8723 × x) = S$1.8723x


If you decide to sell these x pounds back,
amount in S$ you would get for it

= S$(1.8267 × x) = S$1.8267x


Percentage loss

= (S$1.8723x - S$1.8267x)/S$1.8723x × 100%

= S$0.0456x / S$1.8723x × 100%

= 0.0456/1.8723 × 100%

= 2.44% (3s.f)

We get the same expression as before.


So matter what x is (whether you have 1 pound left, or even if you didn't even spend any pounds), the percentage loss is the same.

What does changes however, is the total loss.

This part iii) actually tests your concept of percentage.