Mathematics • Year 10 • Unit 1 • Lesson 6
Compound Interest in the Real World
Use A = P(1 + R)ⁿ in real Australian contexts: a HECS-HELP-style savings goal, a Super contribution, an ING Savings Maximiser, a credit-card balance, and the dramatic effect of starting early. Then explain your method.
1. Word problems
Each problem uses the compound interest formula A = P(1 + R)ⁿ from Lesson 6. Remember: R is the rate per compounding period (as a decimal) and n is the total number of compounding periods. Show your working.
1.1 — Saving for a car. Mia wants to buy a used Toyota Corolla in 4 years. She deposits $7,500 today into a term deposit earning 4.6% p.a. compounded annually.
(a) How much will be in the account after 4 years?
(b) The car she wants will cost about $10,000 by then. Does she have enough? By how much is she short or over? 3 marks
1.2 — ING Savings Maximiser (monthly compounding). Ethan deposits $3,000 into an ING Savings Maximiser advertising 5.4% p.a. compounded monthly. He plans to leave it untouched for 2 years.
(a) What is the monthly rate R, and what is n?
(b) How much will be in the account after 2 years?
(c) How much interest has Ethan earned? 3 marks
1.3 — Super at age 15 vs age 25. Layla's grandparents put $5,000 into a super-style fund for her when she is 15. The fund earns 7% p.a. compounded annually. Layla can access it at age 65.
(a) How much will the $5,000 grow to by age 65 (50 years of compounding)?
(b) If they had waited until Layla was 25 to put the $5,000 in (so it only compounds for 40 years), how much would it grow to?
(c) What is the dollar cost of waiting 10 years to start? 4 marks
1.4 — Credit-card debt (compounding works against you). Jordan owes $2,400 on a credit card charging 18% p.a. compounded monthly. He makes no repayments for one full year.
(a) What is the monthly rate, and what is n?
(b) How much does Jordan owe after 1 year?
(c) How much interest has been added in that year? 3 marks
1.5 — Annual vs daily compounding. $10,000 is invested at 6% p.a. for 3 years. Compare:
(a) Total amount with annual compounding.
(b) Total amount with daily compounding (365 periods per year).
(c) How much more does daily compounding earn? Does the lesson's claim that "more frequent compounding gives more interest" hold here? 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 Two students invest $5,000 each at 4% p.a. for 10 years. Sam uses simple interest. Priya uses compound interest (annual). They both correctly write down their formulas, but Sam claims "after 10 years we'll have the same total because the rate and time are the same." In your own words, explain (i) why Sam is wrong, (ii) what the lesson calls the source of the gap between simple and compound, and (iii) calculate both final amounts to back up your explanation.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Saving for a car
(a) A = 7,500 × (1.046)⁴ = 7,500 × 1.197437 = $8,980.78.
(b) Short by $10,000 − $8,980.78 = $1,019.22. Mia needs to save more or wait a bit longer.
1.2 — ING Savings Maximiser (monthly)
(a) R = 0.054 ÷ 12 = 0.0045 per month; n = 2 × 12 = 24.
(b) A = 3,000 × (1.0045)²⁴ = 3,000 × 1.113735 = $3,341.21.
(c) Interest = 3,341.21 − 3,000 = $341.21.
1.3 — Super: starting at 15 vs 25
(a) Start at 15, 50 years: A = 5,000 × (1.07)⁵⁰ = 5,000 × 29.4570 = $147,285.13.
(b) Start at 25, 40 years: A = 5,000 × (1.07)⁴⁰ = 5,000 × 14.9745 = $74,872.45.
(c) Cost of waiting 10 years: 147,285.13 − 74,872.45 = $72,412.68. That's the same $5,000 — just 10 more years of compounding. This is why "start early" is the most important rule for super.
1.4 — Credit-card debt
(a) Monthly rate = 0.18 ÷ 12 = 0.015; n = 12 months.
(b) Balance owing = 2,400 × (1.015)¹² = 2,400 × 1.195618 = $2,869.48.
(c) Interest added = 2,869.48 − 2,400 = $469.48. Compound interest cuts both ways — at 18% it makes debts explode.
1.5 — Annual vs daily compounding
(a) Annual: A = 10,000 × (1.06)³ = 10,000 × 1.191016 = $11,910.16.
(b) Daily: R = 0.06 ÷ 365; n = 1,095. A = 10,000 × (1 + 0.06/365)¹⁰⁹⁵ ≈ 10,000 × 1.197199 = $11,971.99.
(c) Difference ≈ $61.83 more from daily. The lesson's claim holds, but the extra is small after 3 years — daily wins by more over decades.
2.1 — Explain your thinking (sample response)
Sam is wrong because simple interest only ever earns interest on the original principal, but compound interest earns interest on interest. After year 1 the two are equal (both add 4% of $5,000 = $200), but from year 2 compound interest is calculated on $5,200 instead of $5,000, so the balance grows faster every year. The lesson calls this gap "interest on interest" — the source of compound interest's power.
Numbers to back it up: Sam (simple) → $5,000 + 5,000 × 0.04 × 10 = $5,000 + $2,000 = $7,000. Priya (compound) → A = 5,000 × (1.04)¹⁰ = 5,000 × 1.480244 = $7,401.22. Priya is $401.22 ahead after 10 years.
Marking: 1 mark for correctly naming "interest on interest"; 1 for noting they tie after year 1; 1 for Sam's $7,000; 1 for Priya's $7,401.22.