Cheryl wants to open a fixed deposit account with either Bank H or Bank L for a period of 4 years. The following are the promotions offered by the two banks. Cheryl deposited $30 000 into Bank H. Calculate the total amount in her account after 4 years. Answer $ ... Cheryl claimed that Bank H offers a better deal than Bank L. Do you agree with Cheryl's claim?
Justify your conclusion with clear calculations. Answer The exchange rate between Singapore Dollars (S$) and Chinese Yuan (CNY) is S$1 = CNY5.33. The exchange rate between Hong Kong dollars (HK$) and Singapore Dollars is HK$1 = S$0.17. Tan is planning a trip to Hong Kong and Guangzhou.
He finds these hotel prices on a website. By comparing the exchange rates, explain which hotel charges a cheaper rate per night.
Show your working clearly. Answer The ... hotel charges a cheaper rate per night. Tan books 4 nights in the Hong Kong hotel and 2 nights in the Guangzhou hotel. He pays using his credit card. The credit card company converts the prices to Singapore dollars and charges a fee of k% for the currency conversion. Given that the total amount Tan pays for the two hotels, including the credit card fee, is $890, find the value of k.

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.

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

$k = 2.232\ldots$

$k \approx 2.23$