Mathematics Standard • Year 11 • Module 3 • Lesson 11
Simple Interest
Apply I = Prn to realistic Australian term deposits, personal loans, and savings plans — including the time-to-target and rate-comparison patterns.
Problem 1 — Term deposit decision
Naomi has $14,500 saved from a casual job. She is choosing between two term deposits offered by an Australian bank, both paying simple interest:
Option A: 3-year term at 4.8% per annum.
Option B: 5-year term at 4.2% per annum.
Set up: What are we solving for?
(i) Calculate the total amount Naomi would receive under Option A. 2 marks
(ii) Calculate the total amount under Option B. 2 marks
(iii) Which option pays a higher total amount, and by how much? State a clear conclusion sentence. 1 mark
Stuck? A = P + I. Compute I for each option then add the same $14,500 principal.Problem 2 — Car loan from a credit union
Daniel borrows $18,400 from a credit union to buy a used car. The loan is at 7.5% per annum simple interest, repayable over 4 years.
Set up: What are we solving for?
(i) Calculate the total interest charged over the 4-year term. 1 mark
(ii) Calculate the total amount Daniel must repay. 1 mark
(iii) If Daniel repays the loan in equal monthly instalments over 48 months, calculate the monthly repayment (assume simple interest is fully accrued and divided evenly across the term). 2 marks
Stuck on (iii)? Monthly repayment = total repayable ÷ 48.Problem 3 — Time to reach a deposit target
Layla wants to save $8,000 for a holiday. She invests $6,800 in a simple interest account paying 5.6% per annum.
Set up: What are we solving for?
(i) Calculate the interest Layla needs to earn to reach her $8,000 target. 1 mark
(ii) Calculate how many years (to 2 d.p.) Layla must wait. 2 marks
(iii) Convert the time into months and round UP to the next whole month. Explain in one sentence why rounding UP (not to the nearest whole month) is appropriate here. 2 marks
Stuck on (iii)? If she rounded DOWN, she would not yet have reached $8,000 — she needs the full target, so always round UP for "time to reach" questions.Problem 4 — Comparing investment options with different principals
Two siblings, Hugo and Sienna, each have money to invest in simple-interest accounts.
Hugo: $9,000 at 5.4% per annum for 4 years.
Sienna: $11,500 at 4.6% per annum for 4 years.
Set up: What are we solving for?
(i) Calculate the interest earned by each sibling over 4 years. 2 marks
(ii) Sienna says, "I earned more interest, so my rate must be higher." Explain in one sentence why this is misleading. 1 mark
(iii) Express each sibling's interest as a percentage of their own principal (i.e. I ÷ P × 100). State which percentage is higher and link back to the original rates. 2 marks
Stuck on (iii)? For 4 years at simple interest, I ÷ P × 100 = 4 × annual rate (in %).Problem 5 — Personal loan reverse-engineering
Marcus took out a 2-year simple-interest personal loan from a small lender. The lender's contract shows the total repayable as $11,440, with $1,440 in interest.
Set up: What are we solving for?
(i) Find the principal Marcus originally borrowed. 1 mark
(ii) Find the annual simple interest rate charged by the lender. 2 marks
(iii) Marcus can take out a similar 2-year loan from his bank at 6.4% per annum simple interest for the same principal. Calculate the bank's total repayable and the dollar saving Marcus makes by choosing the bank. 2 marks
Stuck on (i)? Principal = Total repayable − Interest. Then use r = I ÷ (Pn) and convert to percentage.How did this worksheet feel?
What I'll revisit before next class:
Problem 1 — Naomi's term deposit
Set up. Compute I for each, add to the $14,500 principal, then compare.
(i) Option A. I = $14,500 × 0.048 × 3 = $2,088. A = $14,500 + $2,088 = $16,588.00.
(ii) Option B. I = $14,500 × 0.042 × 5 = $3,045. A = $14,500 + $3,045 = $17,545.00.
(iii) Difference = $17,545 − $16,588 = $957. Option B pays $957 more in total. (The extra 2 years more than compensates for the 0.6 percentage point lower rate.)
Problem 2 — Daniel's car loan
Set up. Apply I = Prn, sum for total repayable, then divide by 48 months for instalments.
(i) I = $18,400 × 0.075 × 4 = $5,520.00.
(ii) A = $18,400 + $5,520 = $23,920.00.
(iii) Monthly = $23,920 ÷ 48 ≈ $498.33 per month. (Real loans use reducing-balance interest so monthly amounts differ; this question assumes the simple-interest total is evenly split.)
Problem 3 — Layla's holiday savings
Set up. Find I needed, then n = I ÷ (Pr), then convert and round.
(i) I needed = $8,000 − $6,800 = $1,200.
(ii) n = $1,200 ÷ ($6,800 × 0.056) = $1,200 ÷ $380.80 ≈ 3.15 years.
(iii) Months = 3.15 × 12 ≈ 37.8 months → round UP to 38 months. We round UP because at 37 months Layla has not quite reached $8,000 — rounding down would leave her short of her target. "At least as much as $8,000" always rounds UP.
Problem 4 — Hugo vs Sienna
Set up. Compute each I, then compare interest-to-principal ratios to fairly compare yields.
(i) Hugo: I = $9,000 × 0.054 × 4 = $1,944. Sienna: I = $11,500 × 0.046 × 4 = $2,116.
(ii) Misleading: Sienna earned more dollars because she invested a larger principal — not because her rate is higher. Comparing raw dollar interest with different principals is unfair.
(iii) Hugo: $1,944 ÷ $9,000 × 100 = 21.6% over 4 years (i.e. 5.4% × 4). Sienna: $2,116 ÷ $11,500 × 100 = 18.4% over 4 years (i.e. 4.6% × 4). Hugo's percentage return is higher (21.6% vs 18.4%) — confirming his 5.4% rate beats Sienna's 4.6% rate.
Problem 5 — Marcus's personal loan
Set up. P = total − interest. Then r = I ÷ (Pn) and compare to bank quote.
(i) P = $11,440 − $1,440 = $10,000.
(ii) r = $1,440 ÷ ($10,000 × 2) = $1,440 ÷ $20,000 = 0.072 → 7.2% per annum.
(iii) Bank: I = $10,000 × 0.064 × 2 = $1,280. Total = $11,280. Marcus would save $11,440 − $11,280 = $160 by borrowing from his bank instead.