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NSWMaths AdvancedQuick questions
Year 12: Financial Mathematics
Quick questions on Simple and compound interest, future value and present value for HSC Maths Advanced
14short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.
What is simple interest?Show answer
Simple interest is paid only on the original principal. After $n$ time periods at per-period rate $r$,
What is compound interest?Show answer
Compound interest is added to the principal at the end of each period and earns interest in subsequent periods. After $n$ compounding periods at per-period rate $r$,
What is per-period rate and number of periods?Show answer
Rates are usually quoted as a nominal annual rate, but interest may compound more often than annually. Convert before applying the formula.
What is present value?Show answer
The present value $P$ is the amount you must invest today to grow to $A$ in $n$ periods. Rearranging,
What is solving for the rate or time?Show answer
Solving $A = P(1 + r)^n$ for $r$ or $n$:
What is effective annual rate?Show answer
The effective annual rate makes different compounding frequencies comparable. If the nominal annual rate is $R$ compounded $m$ times per year,
What is simple vs compound?Show answer
Compare $\$1000$ at $5\%$ per annum for $10$ years under simple and compound interest (annual compounding).
What is quarterly compounding?Show answer
$\$8000$ at $4\%$ per annum compounded quarterly for $3$ years.
What is solving for time?Show answer
How long does it take $\$2000$ to double at $7\%$ per annum compounded annually?
What is using the annual rate with monthly periods?Show answer
If interest compounds monthly, the rate in the formula is $R / 12$, not $R$. The number of periods is months, not years.
What is mixing up simple and compound?Show answer
A linear question uses $A = P(1 + r n)$. An exponential question uses $A = P(1 + r)^n$. Read the wording carefully.
What is forgetting to discount?Show answer
A present value question asks for the amount today, so divide by $(1 + r)^n$ (or multiply by $(1 + r)^{-n}$).
What is mis-rounding intermediate steps?Show answer
Carry the unrounded compound factor to the final calculation, then round to cents at the end. Rounding $(1.005)^{48}$ to $1.27$ instead of $1.27049$ shifts the answer by several dollars.
What is confusing nominal and effective rates?Show answer
A nominal $12\%$ compounded monthly is an effective $12.68\%$. The two are not interchangeable.