Number 9
4 marks · HardIn the table below are some exchange rates:
| Currency | Exchange rate to $1 (USD) |
|---|---|
| UK Pound (£) | 0.70 |
| Japanese Yen (¥) | 154.50 |
| South African Rand (R) | 16.78 |
A student has ¥30,900 (Japanese yen). She wants to convert her money first to US dollars, and then use all of her dollars to buy UK pounds. Work out how many UK pounds (£) she will get. Give your answer to the nearest pound.
Explain why she will not get exactly the same number of pounds if she first converts her yen to South African rand, and then all her rand to US dollars, and finally all her dollars to UK pounds.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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(a) £140 £
(b) Exchange rates between currencies may not be consistent in all directions; converting through different currencies can result in a different total due to rate conversion loss. · must show recognition that indirect conversion might yield a different amount due to varying exchange rates
Common mistakes: Incorrect order of conversion; Incorrect exchange calculation; Omitting rounding
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Divides 30,900 yen by 154.50 to obtain amount in US dollars.
M2 (a) · 1 mark · Uses exchange rate to convert dollars to pounds correctly (divides dollar amount by 1/0.70, or multiplies by 0.70). (follow-through)
A1 (a) · 1 mark · Gives correct answer to the nearest pound (£140). (follow-through)
B1 (b) · 1 mark · Clearly explains that due to differences in exchange rates and possible conversion losses, indirect conversions often do not result in the same value.
Worked solution
a) First, convert yen to US dollars:
Next, convert US dollars to UK pounds:
So, she will get £140 (to the nearest pound).
b) If she converts through South African rand, the intermediate steps and rates may not perfectly reverse when exchanged again, leading to rounding and different exchange rates causing a different final amount. So, the process is not always reversible and direct/indirect conversions don't yield the same result due to these fluctuations.