Financial mathematics (HSC Maths Standard 2) quiz

Using $FV = PV(1 + r)^n$, the future value of $8000$ dollars invested at $4\%$ per annum compounded annually for $6$ years is closest to:

A $5$-year loan compounds quarterly at $8\%$ per annum. What is the per-period rate $r$ and the number of periods $n$?

A machine costing $24{,}000$ dollars depreciates by the declining-balance method at $20\%$ per annum. Using $V = P(1 - r)^n$, its book value after $4$ years is:

A new vehicle costs $56{,}000$ dollars and depreciates by straight-line at $6000$ dollars per year. Using $V = P - Dn$, its value at the end of year $5$ is:

The CPI was $114.8$ in June 2019 and $138.8$ in June 2024. The average annual inflation rate over the $5$ years, using $\left(\frac{CPI_2}{CPI_1}\right)^{1/n} - 1$, is closest to:

Sam pays $300$ dollars at the end of each month into an account earning $4.8\%$ per annum compounded monthly for $10$ years. Using $FV = M\left[\frac{(1 + r)^n - 1}{r}\right]$ with $r = 0.004$ and $n = 120$, the future value is closest to:

A first-home buyer wants $120{,}000$ dollars in $5$ years from an account paying $4.5\%$ per annum compounded monthly. Using $PV = \frac{FV}{(1 + r)^n}$ with $r = 0.00375$ and $n = 60$, the lump sum needed today is closest to:

A $400{,}000$-dollar home loan is taken at $6\%$ per annum compounded monthly over $25$ years. Using $M = \frac{Pr}{1 - (1 + r)^{-n}}$ with $r = 0.005$ and $n = 300$, the monthly repayment is closest to:

A bank share trades at $98$ dollars and pays an annual dividend of $4.80$ dollars per share. Its dividend yield, found by $\frac{\text{dividend per share}}{\text{share price}} \times 100\%$, is closest to:

A loan of $15{,}000$ dollars is repaid monthly at $300$ dollars with $r = \frac{0.04}{12}$. Using $B_n = B_{n-1}(1 + r) - M$, the balance immediately after the first repayment is closest to: