\subsection{Review of Percentages}
\begin{enumerate}
    \item Express each percentage as a decimal.
        \begin{enumerate}[(a)]\begin{multicols}{3}
            \item \(175 \%\)
            \item \(0.6 \%\)
            \item \(142.6 \%\)
            \item \(\frac{1}{4} \%\)
            \item \(56 \%\)
            \item \(75 \%\)
            \item \(37 \frac{1}{2} \%\)
            \item \(16 \frac{2}{3} \%\)
            \item \(6.4 \%\)
        \end{multicols}\end{enumerate}
    \item Express each fraction or decimal as a percentage.
        \begin{enumerate}[(a)]\begin{multicols}{3}
            \item \(\frac{3}{8}\)
            \item \(\frac{9}{16}\)
            \item \(2 \frac{1}{4}\)
            \item \(\frac{2}{3}\)
            \item \(\frac{4}{3}\)
            \item \(\frac{3}{400}\)
            \item 0.04
            \item 0.015
            \item 1.175
        \end{multicols}\end{enumerate}
    \item Evaluate these amounts, correct to 2 decimal places where necessary.
        \begin{enumerate}[(a)]\begin{multicols}{3}
            \item \(26 \%\) of 264
            \item \(138.5 \%\) of 650
            \item \(150 \%\) of 846
        \end{multicols}\end{enumerate}
    \item Evaluate these amounts, correct to the nearest cent where necessary.
        \begin{enumerate}[(a)]\begin{multicols}{3}
            \item \(23.7 \%\) of \(\$ 960\)
            \item \(3.2 \%\) of \(\$ 1500\)
            \item \(0.25 \%\) of \(\$ 800\)
            \item \(6 \frac{1}{2} \%\) of \(\$ 200\)
            \item \(\frac{1}{4} \%\) of \(\$ 840\)
            \item \(7.25 \%\) of \(\$ 1600\)
        \end{multicols}\end{enumerate}
    \item Find what percentage the first quantity is of the second quantity, correct to 1 decimal place.
        \begin{enumerate}[(a)]\begin{multicols}{3}
            \item \(7 \mathrm{~km}, 50 \mathrm{~km}\)
            \item \(\$ 4, \$ 200\)
            \item \(14 \mathrm{~kg}, 400 \mathrm{~kg}\)
        \end{multicols}\end{enumerate}
    \item Find what percentage the first quantity is of the second quantity, correct to 2 decimal places where necessary. You will need to express both quantities in the same unit first.
        \begin{enumerate}[(a)]\begin{multicols}{3}
            \item \(3.4 \mathrm{~cm}, 2 \mathrm{~m}\)
            \item 8 hours, 2 weeks
            \item \(250 \mathrm{~m}, 4 \mathrm{~km}\)
            \item 1 day, 1 year
            \item 33 weeks, 1 century
            \item 5 apples, 16 dozen apples
        \end{multicols}\end{enumerate}
    \item A sample of a certain alloy weighs \(1.6 \mathrm{~g}\).
        \begin{enumerate}[(a)]
            \item Aluminium makes up \(48 \%\) of the alloy. What is the weight of the aluminium in the sample?
            \item The percentage of lead in the alloy is \(0.23 \%\). What is the weight of the lead in the sample?
        \end{enumerate}
    \item Carbon dioxide makes up \(0.059 \%\) of the mass of the Earth's atmosphere. The total mass of the atmosphere is about 5 million megatonnes. What is the total mass of the carbon dioxide in the atmosphere?
\end{enumerate}

\subsection{Using Percentages}

\begin{enumerate}
    \item What percentage of the total cost is a deposit of:
        \begin{enumerate}[(a)]
            \item \(\$ 33\) on a television valued at \(\$ 550\) ?
            \item \(\$ 124.10\) on a stove valued at \(\$ 1460\) ?
        \end{enumerate}
    \item Find the selling price if the commission and the commission rate are as given.
        \begin{enumerate}[(a)]\begin{multicols}{2}
            \item Commission \(\$ 35\), rate \(7 \%\)
            \item Commission \(\$ 646\), rate \(3.4 \%\)
            \item Commission \(\$ 16586.96\), rate \(5.2 \%\)
            \item Commission \(\$ 3518.61\), rate \(11.4 \%\)
        \end{multicols}\end{enumerate}
    \item Find, to 1 decimal place, the percentage profit or loss on costs in these situations.
        \begin{enumerate}\begin{multicols}{2}
            \item Costs \(\$ 16000\) and sales \(\$ 18000\)
            \item Costs \(\$ 162000\) and sales \(\$ 150000\)
            \item Costs \(\$ 2800000\) and sales \(\$ 3090000\)
            \item Costs \(\$ 289000000\) and sales \(\$ 268000000\)
        \end{multicols}\end{enumerate}
\end{enumerate}

\subsection{Simple Interest}

\begin{enumerate}
    \item Calculate the missing entries for these simple interest investments.
        \begin{center}
        \begin{tabular}{|c|c|c|c|c|}
        \hline
        & Principal & Rate p.a. & Time in years & Total interest \\
        \hline
        a & \(\$ 10000\) & \(8 \%\) &  & \(\$ 3200\) \\
        \hline
        b & \(\$ 4400000\) & \(7 \frac{1}{2} \%\) &  & \(\$ 3960000\) \\
        \hline
        c & \(\$ 5000\) &  & 6 & \(\$ 1350\) \\
        \hline
        d & \(\$ 260000\) &  & 8 & \(\$ 83200\) \\
        \hline
        e &  & \(6 \%\) & 5 & \(\$ 900\) \\
        f &  & \(3.6 \%\) & 4 & \(\$ 115.20\) \\
        \hline
        \end{tabular}
        \end{center}
    \item Sartoro invested \(\$ 80000\) in a building society that pays \(6.5 \%\) p.a. simple interest. Over the years, the investment has paid him \(\$ 57200\) in interest. How many years has he had the investment?
    \item Madeline has received \(\$ 168000\) in total simple interest payments on an investment of \(\$ 400000\) that she made six years ago. What rate of interest has the bank been paying?
    \item An investor wishes to earn \(\$ 240000\) interest over a five-year period from an account that earns \(12.5 \%\) p.a. simple interest. How much does the investor have to deposit into the account?
\end{enumerate}

\subsection{Percentage Increase \& Decrease}

\begin{enumerate}
    \item Rainfall across one state has decreased over the last five years by about \(24 \%\). By multiplying by \(76 \%=0.76\), estimate, correct to the nearest \(10 \mathrm{~mm}\), the annual rainfall this year at a place where the rainfall five years ago was:
        \begin{enumerate}\begin{multicols}{2}
            \item \(1000 \mathrm{~mm}\)
            \item \(250 \mathrm{~mm}\)
            \item \(680 \mathrm{~mm}\)
            \item \(146 \mathrm{~mm}\)
        \end{multicols}\end{enumerate}
    \item Admissions to different wards of St Luke's Hospital mostly rose from 2006 to 2007, but by quite different percentage amounts. Find the percentage increase or decrease in wards where the numbers during 2006 and 2007, respectively, were:
        \begin{enumerate}\begin{multicols}{2}
            \item 50 and 68
            \item 120 and 171
            \item 92 and 77
            \item 24 and 39
        \end{multicols}\end{enumerate}
    \item Radix Holdings Pty Ltd recently issued bonus shares to its shareholders. Each shareholder received an extra \(12 \%\) of the number of shares currently held. Find the original holding of a shareholder who now holds:
        \begin{enumerate}\begin{multicols}{2}
            \item 672 shares
            \item 4816 shares
            \item 1000 shares
            \item 40200 shares
        \end{multicols}\end{enumerate}
    \item A research institute is trying to find out how much water Lake Grendel had 1000 years ago. The lake now contains 24000 megalitres, but there are various conflicting theories about the percentage change over the last 1000 years. Find how much water the lake had 1000 years ago, correct to the nearest 10 megalitres, if in the last 1000 years the volume has:
        \begin{enumerate}\begin{multicols}{2}
            \item risen by \(80 \%\)
            \item fallen by \(28 \%\)
            \item risen by \(140 \%\)
            \item fallen by \(4 \%\)
        \end{multicols}\end{enumerate}
\end{enumerate}

\subsection{Repeated Increase \& Decrease}

\begin{enumerate}
    \item Shares in the Metropolitan Brickworks have been falling by \(23 \%\) per year for the last five years. Find the present worth of a parcel of shares whose original worth five years ago was:
        \begin{enumerate}\begin{multicols}{2}
            \item \(\$ 1000\)
            \item \(\$ 120000\)
            \item \(\$ 25660\)
            \item \(\$ 3860000\)
        \end{multicols}\end{enumerate}
    \item
        \begin{enumerate}
            \item A shirt is discounted by \(50 \%\) and the resulting price is then increased by \(50 \%\). By what percentage is the price increased or decreased from its original value?
            \item The price of a shirt is increased by \(50 \%\) and the resulting price is then decreased by \(50 \%\). By what percentage is the price increased or decreased from its original value?
            \item Can you explain the relationship between your answers to parts \(\mathbf{a}\) and \(\mathbf{b}\) ?
        \end{enumerate}
    \item A book shop has a \(50 \%\) sale on all stock, and has a container of books with the sale price reduced by a further factor of \(16 \%\).
        \begin{enumerate}
            \item What was the total discount on each book in the container?
            \item If a book in the container is now selling for \(\$ 10.50\), what was its original price?
        \end{enumerate}
    \item A particular strain of bacteria increases its population on a certain prepared Petri dish by \(34 \%\) every hour. Calculate the size of the original population four hours ago if there are now 56000 bacteria.

\end{enumerate}

\subsection{Compound Interest}

\begin{enumerate}
    \item[]
        \begin{enumerate}
            \item Find the compound interest on \(\$ 1000\) at 5\% p.a., compounded annually for 200 years.
            \item Find the simple interest on \(\$ 1000\) at \(5 \%\) p.a. for 200 years.
        \end{enumerate}
    \item \(\$ 10000\) is borrowed for five years and compound interest at \(10 \%\) p.a. is charged by the lender.
        \begin{enumerate}
            \item How much money is owed to the lender after the five-year period?
            \item How much of this amount is interest?
        \end{enumerate}
    \item Money borrowed at \(8 \%\) p.a. interest, compounded annually, grew to \(\$ 100000\) in four years.
        \begin{enumerate}
            \item Find the total percentage increase.
            \item Hence find the original amount invested.
        \end{enumerate}
    \item A man now owes the bank \(\$ 56000\), after having taken out a loan five years ago. Find the original amount that he borrowed if the rate of interest per annum, compounded annually, has been:
        \begin{enumerate}\begin{multicols}{2}
            \item \(3 \%\)
            \item \(5.6 \%\)
            \item \(9.25 \%\)
            \item \(15 \%\)
        \end{multicols}\end{enumerate}
    \item Ms Smith invested \(\$ 50000\) at \(6 \%\) p.a. interest, compounded annually, for four years. The tax department wants to know exactly how much interest she earned each year. Calculate these figures for Ms Smith.
    \item Mrs Robinson has taken out a loan of \(\$ 300000\) at \(8 \%\) p.a. interest, compounded annually, for four years. She wants to know exactly how much interest she will be charged each year so that she can include it as a tax deduction in her income tax return. Calculate these figures for Mrs Robinson.

\end{enumerate}

\subsection{Depreciation}

\begin{enumerate}
    \item The Hungry Hour Cafe purchased an air-conditioning system six years ago for \(\$ 250000\), and is assuming a depreciation rate of \(20 \%\).
        \begin{enumerate}
            \item Find the value after one year.
            \item Find the value after two years.
            \item Find the value after six years.
            \item What is the percentage decrease in value over the six years?
            \item What is the average depreciation, in dollars p.a., on the air-conditioning system over the six years?
        \end{enumerate}
    \item The Backyard Rubbish Experts bought a fleet of small trucks for \(\$ 1340000\) and depreciated them at \(22.5 \%\) p.a. Five years later they sold them for \(\$ 310000\). Was the price that they obtained better or worse than the depreciated value, and by how much?
    \item A landlord spent \(\$ 3400\) on vacuum cleaners for his block of home units and depreciated them for taxation purposes at \(25 \%\) p.a. Find their value at the end of each of the first three years, and the amount of the depreciation that the landlord could claim against his taxable income for each of those three years.
    \item Lara and Kate each received \(\$ 100000\) from their parents. Lara invested the money at \(6.2 \%\) p.a. compounded annually, whereas Kate bought a luxury car that depreciated at a rate of \(20 \%\) p.a. What were the values of their investments at the end of five years?
    \item Taxis depreciate at \(50 \%\) p.a., and other cars depreciate at \(22.5 \%\) p.a.
        \begin{enumerate}
            \item What is the total percentage depreciation on each type of vehicle after seven years?
            \item What is the difference in value, to the nearest dollar, after seven years of a fleet of taxis and a fleet of other cars, if both fleets cost \(\$ 1000000\) ?
        \end{enumerate}
\end{enumerate}