Question 18
When a child is born, their parent deposits $3000 to open an investment account earning interest at 4.2% p.a. compounding monthly. If there are no further transactions and the interest rate does not change, calculate the amount of interest earned by the child’s 18th birthday.
Count in months, grow the deposit, then take the deposit back off
Watch 18 years of monthly compounding build on the deposit. The grey block is the money the parent put in. Only the orange part above it is interest.
The rate and the count must match the compounding. Monthly means 0.0035 per month for 216 months. The rule gives the value of the account, and the interest is what is left once the deposit is taken away.
Choose $i$, $n$ and the rule, then answer what was asked
Make the four decisions this question needs. The panel runs your calculation, and the bars compare your answer with the interest the account really earns.
Make all four choices. The phrase “compounding monthly” decides $i$ and $n$, and the last line of the question decides your final answer.
$I=Pin$ is simple interest. It only ever pays interest on the original $3000. Compounding means each month’s interest starts earning interest too, so use the formula book’s compound interest rule, $A=P(1+i)^n$.
0.042 is the yearly rate. Adding 4.2% every month for 216 months turns $3000 into more than 21 million dollars, which should set off alarm bells. Divide by 12 first: $i=0.0035$.
That is yearly compounding, 4.2% added once a year for 18 years. This account compounds monthly, so interest is added twelve times a year and it earns a little more. Use the monthly rate and count in months.
Your rate is per month, but 18 counts years, so this is only 18 months of interest. Count the periods in months: $n=18\times12=216$.
Your calculation is right, but $6380.79 is what the account is worth on the 18th birthday. The question asks for the interest earned, so subtract the $3000 that was deposited.
That’s it. Monthly rate, months counted, compound rule, then the deposit taken off. The account grows to $6380.79, so the interest earned is $3380.79.
Work through the solution one mark at a time
Try each step yourself before you reveal it. There is a mark for $i$ and $n$, one for the substitution, one for the value of the account and one for the interest.
Interest compounds monthly, so work per month. Write down every value before you substitute.
$$P=3000,\qquad i=\frac{0.042}{12}=0.0035,\qquad n=18\times12=216$$
This mark may be implied by your later working, so a correct substitution earns it even if you skip this line. Write it anyway. The 2024 subject report held up a response that named $i$ and $n$ before substituting as the model for this question.
Marker: correctly determines the $i$ and $n$ values
Use the compound interest rule from the formula book and put your values in.
$$A=P(1+i)^n=3000\times(1+0.0035)^{216}$$
Follow-through applies, so if your $i$ or $n$ had a slip, substituting your own values correctly still earns this mark. Type it into your calculator in one line, with the 216 as the power.
Marker: substitutes into appropriate rule
Evaluate it. This is the value of the account on the 18th birthday.
$$A=6380.7928\ldots\approx6380.79$$
The guide accepts appropriate rounding here, for example to the nearest cent, nearest 5 cents or nearest dollar. Keep the cents, since the subject report asks for money values not rounded beyond the nearest cent.
Marker: determines value of investment
The question asks for the interest, so take the deposit back off on its own labelled line.
$$I=A-P=6380.79-3000=3380.79$$
The guide accepts alternative approaches, such as writing the whole thing in one line as $I=3000(1.0035)^{216}-3000$. Whichever way you go, finish with a sentence in dollars and cents.
Marker: determines amount of interest earned
Each phrase of the question gave you something
One deposit, one rate, no payments in or out. That is the compound interest rule with nothing added, and it is in the formula book. The 2024 subject report printed a response to this question as a model. It named the monthly rate and the number of months, substituted into the stated rule, and worked out the interest on its own clearly labelled line, rounded to the cent.
If I had to guess where you might lose marks, it would be the last line. After a long calculation it is easy to stop at $6380.79, but that is the value of the account and the question asks for the interest. The other easy slips are in the first line: using 18 for $n$ when $i$ is a monthly rate, or forgetting to divide 4.2% by 12. Write $P$, $i$ and $n$ down before you substitute, then reread the question before you write your final sentence.
Only mark this done when you could do it without help. Reading the solution does not count.
Question wording and marking-guide steps are from the 2024 QCAA General Mathematics external assessment, © State of Queensland (QCAA) 2024, licensed under CC BY 4.0, and have been adapted. Tangent Tuition is not affiliated with the QCAA.
Spot a mistake on this page? Report it