Mrs Boey deposited $\char36{}20 000$ in a bank that pays 0.8% per annum compound interest compounded half-yearly. Find the total amount of money she will receive at the end of 5 years, leaving your answer to the nearest cent. Shane and Glen came across an article in the newspaper with the headline shown above and made the following comments. Shane: Oh no, the GST will increase by 2% soon! Glen: No! I disagree. It did not increase by 2%, in fact it is MORE than 2%! Whose statement is correct? Support your answer with mathematical calculations.

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.