Boey 夫人将 $\char36{}20 000$ 存入银行，该银行每半年结算一次复利，年利率为 0.8%。求她在 5 年结束时将收到的总金额，答案保留到最近的分。 Shane 和 Glen 看到报纸上有一篇标题如上文所示的文章，并发表了以下评论。 Shane：不妙，消费税（GST）很快就要增加 2% 了！ Glen：不！我不同意。它不是增加了 2%，事实上比 2% 还要多！ 谁的说法正确？请用数学计算来支持你的答案。

1. Find the half-yearly interest rate and the total number of compounding periods.

Since the annual interest rate is $0.8\%$ and it is compounded half-yearly,

half-yearly rate $= \dfrac{0.8\%}{2} = 0.4\% = 0.004$.

Over $5$ years, number of half-yearly periods $= 5 \times 2 = 10$.

2. Apply the compound interest formula and round to the nearest cent.

$A = 20000(1+0.004)^{10}$

$A = 20000(1.004)^{10}$

$A = 20809.495\ldots$

To the nearest cent, the total amount is $\char36{}20\,809.50$.

1. Find the change in GST rate from the headline.

GST is raised from $7\%$ to $9\%$.

Increase in GST rate $=9\%-7\%=2\%$ points.

2. Calculate the percentage increase relative to the original GST rate and decide whose statement is correct.

Percentage increase relative to the original GST rate
$=\frac{9-7}{7}\times 100\%$
$=\frac{2}{7}\times 100\%$
$=28.571\ldots\%\approx 28.6\%.$

Since $28.6\%>2\%$, the increase is more than $2\%$ of the original GST rate.