Mathematics • Year 10 • Unit 1 • Lesson 5
Simple Interest in the Real World
Apply the simple-interest formula I = PRT to realistic Australian savings, term deposits and personal loans — from CBA term deposits to short-term lenders. Each problem requires you to identify P, R and T (converting time to years and rates to decimals) and to interpret the answer for a real saver or borrower. Then explain your method in your own words.
1. Word problems
Each problem uses I = PRT or a rearrangement (to find P, R or T) from Lesson 5. Always convert R to a decimal and T to years before substituting. Show your working — a final answer with no working only earns half marks.
1.1 — Six-month term deposit. Aisha deposits $10,000 in a Commonwealth Bank term deposit at 4.5% per annum simple interest for 6 months (the lesson's real-world anchor).
(a) Convert the time to years and the rate to a decimal.
(b) Calculate the interest earned.
(c) Calculate the total amount at maturity. 3 marks
1.2 — Personal loan for a used car. Lucas borrows $14,000 to buy a second-hand Toyota at 9.2% p.a. simple interest, to be repaid over 3 years.
(a) Calculate the total interest Lucas will pay.
(b) Calculate the total amount he will repay over the 3 years.
(c) If he repays in equal monthly instalments, what is the size of each payment? 3 marks
1.3 — Working backwards from interest earned. Sienna's term deposit paid 5.2% p.a. simple interest. Over 2 years she earned $416 in interest.
(a) Identify which variable in I = PRT is unknown.
(b) Calculate the principal she originally deposited.
(c) Calculate the total amount at maturity. 3 marks
1.4 — Comparing two short-term deposits. A bank offers two short-term deposits on $25,000:
- Option A: 4.8% p.a. simple interest for 6 months.
- Option B: 4.4% p.a. simple interest for 12 months.
(a) Calculate the interest earned under each option.
(b) Calculate the equivalent return per month under each option.
(c) Which option earns more per month, and by how much? 3 marks
1.5 — Short-term lender vs bank. An online short-term lender quotes a rate of 18% p.a. simple interest. Mateo borrows $2,000 for 90 days (use 365 days per year, as the lesson specifies).
(a) Convert 90 days to years (as a fraction or decimal).
(b) Calculate the simple interest Mateo will pay.
(c) Compare this with the interest he would have paid at a bank personal loan rate of 9.5% p.a. for the same 90 days — what extra dollar cost does the short-term lender impose? 3 marks
2. Explain your thinking
This question is about communication, not just numbers. Use full sentences. 4 marks
2.1 A classmate writes: "I worked out the simple interest on $4,000 at 5% for 3 years by computing 4,000 × 5 × 3 = $60,000. That's a great return!". In your own words, explain (i) what went wrong, (ii) which conversion was missed, (iii) what the correct interest should be, and (iv) why the answer "$60,000 in interest on $4,000" should immediately have looked wrong. Refer to "R must be a decimal, not a raw percentage" somewhere in your explanation.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — 6-month CBA term deposit
(a) T = 6 ÷ 12 = 0.5 years. R = 0.045.
(b) I = 10,000 × 0.045 × 0.5 = $225.
(c) A = $10,000 + $225 = $10,225.
This is exactly the lesson's anchor calculation.
1.2 — Personal loan for a used car
(a) I = 14,000 × 0.092 × 3 = 1,288 × 3 = $3,864 in interest.
(b) A = $14,000 + $3,864 = $17,864 total repaid.
(c) Monthly payment = $17,864 ÷ 36 = $496.22 per month (to nearest cent).
1.3 — Find the principal
(a) The unknown is P (the principal).
(b) P = I ÷ (R × T) = 416 ÷ (0.052 × 2) = 416 ÷ 0.104 = $4,000.
(c) A = $4,000 + $416 = $4,416.
1.4 — Comparing two term deposits
(a) Option A: I = 25,000 × 0.048 × 0.5 = $600. Option B: I = 25,000 × 0.044 × 1 = $1,100.
(b) Per month: Option A = $600 ÷ 6 = $100/month. Option B = $1,100 ÷ 12 ≈ $91.67/month.
(c) Option A earns more per month, by $100 − $91.67 = $8.33. So if you can roll over Option A into another deposit, it gives a better monthly return, even though Option B has a longer term.
1.5 — Short-term lender vs bank
(a) T = 90 ÷ 365 years.
(b) Lender: I = 2,000 × 0.18 × (90 ÷ 365) = 360 × (90 ÷ 365) ≈ $88.77.
(c) Bank: I = 2,000 × 0.095 × (90 ÷ 365) = 190 × (90 ÷ 365) ≈ $46.85. Extra cost from short-term lender = $88.77 − $46.85 = $41.92.
Even over just 90 days, the higher rate costs nearly twice as much. Over a year the gap is huge.
2.1 — Explain your thinking (sample response)
My classmate has forgotten the most important conversion in I = PRT: R must be a decimal, not a raw percentage. They used R = 5 instead of R = 0.05, which makes the answer exactly 100 times too big. The correct calculation is I = 4,000 × 0.05 × 3 = $600 over 3 years, not $60,000. Their answer should have looked wrong straight away because $60,000 of interest on a $4,000 deposit is 1,500% return — no real bank pays anywhere near that, especially over only 3 years. A good sanity-check rule: simple interest at a few percent per year should give a few percent of the principal back each year — so on $4,000 you'd expect a few hundred dollars after a couple of years, not tens of thousands.
Marking: 1 for identifying the missing conversion; 1 for using "R must be a decimal"; 1 for the correct $600 answer; 1 for the realism check (e.g. "$60k on $4k is implausible").