Mathematics Standard • Year 11 • Module 3 • Lesson 11
Simple Interest
Practise HSC Mathematics Standard 2-style writing on Simple Interest — short answers and one structured extended response covering rate, time, and comparison.
1. Short-answer questions
1.1 An investor deposits $11,200 in a 3-year term deposit at 4.7% per annum simple interest. Calculate the total amount at maturity. 2 marks Band 3
1.2 An $8,000 loan is charged $1,344 in simple interest over 24 months.
(a) Convert the time to years.
(b) Find the annual interest rate (%). 3 marks Band 3-4
1.3 Mira invests $4,500 at 5.4% per annum simple interest. She wants the investment to reach $5,400.
(a) Calculate the interest needed.
(b) Calculate the time (in years and months, rounded UP to the next whole month) required to reach this target.
(c) Explain in one sentence why rounding UP is essential for "time to reach a target" questions. 4 marks Band 4
2. Extended response
2.1 Owen is comparing three simple-interest options for his $12,000 inheritance. All are quoted per annum:
Option P: Bank A — 3-year term deposit at 5.0% p.a.
Option Q: Bank B — 5-year term deposit at 4.4% p.a.
Option R: Credit union — 4-year term deposit at 4.8% p.a., but with a one-off $250 account-opening fee deducted from the principal before interest accrues.
(a) Calculate the interest earned and the total amount returned under Option P and Option Q.
(b) Calculate the total amount returned under Option R (remembering the $250 fee reduces the principal earning interest).
(c) Rank the three options from highest to lowest total return, and state the dollar gap between the best and worst option. Briefly comment on whether Owen should choose the highest return or whether the term length is also worth considering. 7 marks Band 5-6
Explicit marking criteria
Part (a) — 2 marks
• 1 mark — correct Option P interest and total.
• 1 mark — correct Option Q interest and total.
Part (b) — 2 marks
• 1 mark — reduces principal to $11,750 before calculating interest.
• 1 mark — correct total return for Option R.
Part (c) — 3 marks
• 1 mark — correctly ranks all three options.
• 1 mark — correct dollar gap between best and worst with clear conclusion sentence.
• 1 mark — sensible one-sentence comment that names a trade-off (e.g. higher return may require longer commitment / locked-up funds).
Your response:
Stuck on (b)? Option R earns interest on $11,750 (not $12,000) but the total returned should still be compared on the same basis as P and Q.How did this worksheet feel?
What I'll revisit before next class:
1.1 — Total amount after 3 years (2 marks)
Sample response.
I = $11,200 × 0.047 × 3 = $1,579.20. A = $11,200 + $1,579.20 = $12,779.20.
Marking notes. 1 mark — correct I (with 0.047, not 4.7). 1 mark — correct A with units. Common error: using r = 4.7 (giving I = $157,920).
1.2 — Rate from interest and time (3 marks)
Sample response.
(a) 24 months ÷ 12 = 2 years.
(b) r = $1,344 ÷ ($8,000 × 2) = $1,344 ÷ $16,000 = 0.084 → 8.4% per annum.
Marking notes. (a) 1 mark — correct conversion to years. (b) 1 mark — correct rearrangement r = I ÷ (Pn). 1 mark — correct percentage with unit "per annum". Common error: forgetting to convert 24 months → 2 years before substituting.
1.3 — Time to reach a target + rounding (4 marks)
Sample response.
(a) I needed = $5,400 − $4,500 = $900.
(b) n (years) = $900 ÷ ($4,500 × 0.054) = $900 ÷ $243 ≈ 3.7037 years.
Months = 3.7037 × 12 ≈ 44.44 months → round UP to 45 months (3 years and 9 months).
(c) At 44 months Mira has not yet reached $5,400; rounding UP guarantees she reaches or exceeds the target. Rounding to the nearest whole month could leave her short by a few dollars.
Marking notes. (a) 1 mark — correct interest needed. (b) 1 mark — correct n (years). 1 mark — correct conversion to months with UP rounding. (c) 1 mark — explanation links rounding UP to "must reach or exceed target".
2.1 — Owen's three options (7 marks): sample Band-6 response with annotations
Sample Band-6 response.
(a) Option P and Option Q.
Option P: I = $12,000 × 0.05 × 3 = $1,800. A = $12,000 + $1,800 = $13,800.00. [1 mark — correct Option P.]
Option Q: I = $12,000 × 0.044 × 5 = $2,640. A = $12,000 + $2,640 = $14,640.00. [1 mark — correct Option Q.]
(b) Option R (with fee).
Effective principal after fee = $12,000 − $250 = $11,750. [1 mark — correctly reduces principal.]
I = $11,750 × 0.048 × 4 = $2,256. A = $11,750 + $2,256 = $14,006.00. [1 mark — correct Option R total.]
(c) Ranking and recommendation.
Ranking from highest to lowest total return:
1. Option Q — $14,640.00 (5-year term)
2. Option R — $14,006.00 (4-year term)
3. Option P — $13,800.00 (3-year term) [1 mark — correct ranking.]
Dollar gap between best and worst = $14,640 − $13,800 = $840. Owen earns $840 more with Option Q than with Option P. [1 mark — correct dollar gap + clear conclusion sentence.]
However, Owen should also consider the term length: Option Q locks his money up for 5 years vs only 3 years for Option P. If he might need his savings sooner — for example to put down a house deposit — the shorter-term Option P may still be preferable despite the lower total return. [1 mark — sensible trade-off comment naming term length / liquidity.]
Total: 7/7.
Band descriptors for marker.
Band 3: Calculates two of three options correctly using I = Prn; misses the fee on Option R OR uses wrong principal. ≈ 3 marks.
Band 4: All three options calculated correctly including the $250 fee reduction; ranking attempted but no comment on trade-offs. ≈ 5 marks.
Band 5: Full calculations + correct ranking + dollar gap, but bare conclusion without naming the term-length trade-off. ≈ 6 marks.
Band 6: Complete: three correct totals, correct ranking, correct dollar gap, AND a sensible one-sentence trade-off comment about term length or liquidity. 7/7.