Back to the full dot-point answer

NSWMaths Standard 2Quick questions

Year 12: Financial Mathematics

Quick questions on Compound interest and investments for HSC Maths Standard 2

13short 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 the compound interest formula?
Show answer
From the NESA reference sheet:
What is per-period rate?
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 PVPV is the amount you must invest today to grow to FVFV in nn periods. Rearranging:
What is solving for the rate or time?
Show answer
$n=log⁡(FV/PV)log⁡(1+r).n = \frac{\log(FV / PV)}{\log(1 + r)}.$
What is effect of compounding frequency?
Show answer
For a fixed nominal rate, more frequent compounding gives a slightly higher effective rate. A nominal 6%6\% compounded:
What is comparing investments?
Show answer
When choosing between two investments at different rates and compounding frequencies, compute the future value at the same horizon (or compute effective annual rates) and compare.
What is present value (Australian context, 2025)?
Show answer
A first-home buyer aims to have \80000foradepositin for a deposit in 5years.Theycanearn years. They can earn 4\%$ per annum compounded annually in a high-interest savings account (similar to current major-bank online saver rates in 2025).
What is solving for time?
Show answer
\10000investedat invested at 5.5\%perannumcompoundedannually.Whendoesitreach per annum compounded annually. When does it reach \2000020000?
What is solving for rate?
Show answer
A \2000investmentgrewto investment grew to \28122812 in 66 years compounded annually. Find the rate.
What is confusing simple and compound interest?
Show answer
Simple interest is linear (A=P(1+rn)A = P(1 + rn)); compound is exponential (A=P(1+r)nA = P(1 + r)^n). They diverge over time.
What is forgetting to discount?
Show answer
A present value question asks for the amount today, so divide by (1+r)n(1 + r)^n.
What is rounding the per-period rate too early?
Show answer
Keep the rate to at least 66 decimal places, or carry it as a fraction. Rounding 0.045/120.045 / 12 to 0.0040.004 instead of 0.003750.00375 skews the final answer noticeably.
What is mis-reading nominal vs effective?
Show answer
A nominal 6%6\% compounded monthly is an effective 6.17%6.17\% per annum. The two are different. :::

All Maths Standard 2Q&A pages