Cheryl 想在银行 H 或银行 L 开设一个为期 4 年的定期存款账户。 以下是这两家银行提供的优惠活动。 Cheryl 将 $30 000 存入银行 H。 计算 4 年后她账户中的总金额。 答：$ ... Cheryl 声称银行 H 提供的优惠比银行 L 更好。 你同意 Cheryl 的说法吗？
请用清晰的计算来证明你的结论。 答： 新加坡元（S$）与人民币（CNY）之间的汇率为 S$1 = CNY5.33。 港元（HK$）与新加坡元之间的汇率为 HK$1 = S$0.17。 陈先生计划去香港和广州旅行。
他在一个网站上找到了这些酒店的价格。 通过对比汇率，解释哪家酒店的每晚房费更便宜。
请清晰地写出计算过程。 答： ... 酒店的每晚房费更便宜。 陈先生预订了香港酒店 4 晚和广州酒店 2 晚。 他使用信用卡付款。信用卡公司将价格转换为新加坡元，并收取 k% 的货币兑换手续费。 已知陈先生支付这两家酒店的总费用（包括信用卡手续费）为 $890，求 k 的值。

1. Split the deposit according to Bank H's interest tiers.

First $10 000 earns $0.05\%$ p.a.

Subsequent amount:
$\$30\,000-\$10\,000=\$20\,000$

2. Find the simple interest earned over 4 years for each portion.

Interest on first $10 000:
$\$10\,000\times 0.05\%\times 4=\$20$

Interest on subsequent $20 000:
$\$20\,000\times 0.95\%\times 4=\$760$

3. Add the total interest to the original deposit.

Total amount after 4 years:
$\$30\,000+\$20+\$760=\$30\,780$

1. State the amount Cheryl would have in Bank H after 4 years.

From part (a)(i), the total amount in Bank H after 4 years is

$\char36{}30\,780$.

2. Calculate the amount Cheryl would have in Bank L after 4 years using compound interest.

For Bank L, compound interest is at $0.8\%$ per annum.

$\text{Amount}=30000(1+0.008)^4$

$=30000(1.008)^4$

$=\$30\,971.58\text{ approximately}$

3. Compare the two amounts and justify the conclusion.

Compare:

$\text{Bank H}=\$30\,780$

$\text{Bank L}=\$30\,971.58$

Since

$30\,971.58>30\,780,$

Bank L gives a higher total amount.

1. Convert the Guangzhou hotel price from CNY to Singapore dollars.

Since S$1 = CNY5.33,

$\text{Guangzhou price} = 825 \div 5.33 = 154.784\ldots$

So the Guangzhou hotel costs about S$154.78 per night.

2. Convert the Hong Kong hotel price from HK dollars to Singapore dollars and compare.

Since HK$1 = S$0.17,

$\text{Hong Kong price} = 825 \times 0.17 = 140.25$

So the Hong Kong hotel costs S$140.25 per night.

Compare:

$140.25 < 154.78$

Therefore, the Hong Kong hotel is cheaper per night.

1. Convert the hotel prices to Singapore dollars and find the total before the credit card fee.

Hong Kong hotel:

$825 \times 0.17 = \char36{}140.25$ per night

Guangzhou hotel:

$825 \div 5.33 = \char36{}154.784\ldots$ per night

For 4 nights in Hong Kong and 2 nights in Guangzhou,

$4(140.25) + 2\left(\frac{825}{5.33}\right) = 870.568\ldots$

Total before fee $= \char36{}870.568\ldots$

2. Find the credit card fee as an amount in Singapore dollars.

Fee charged:

$890 - 870.568\ldots = 19.431\ldots$

So the credit card fee is $\char36{}19.431\ldots$.

3. Express the fee as a percentage of the total cost before the fee.

$k = \frac{19.431\ldots}{870.568\ldots} \times 100$

$k = 2.232\ldots$

$k \approx 2.23$