Mathematics • Year 10 • Unit 1 • Lesson 5
Simple Interest, Skill Drill
Build fluency with the simple interest formula from Lesson 5: I = P × R × T (with R as a decimal and T in years). Also the total amount A = P + I and the rearrangements to find P, R or T. One step at a time, fully worked example, guided practice, then independent problems.
1. I do, fully worked example
Read every line. Each step has a short reason on the right so you can see why, not just what.
Problem. Liam invests $5,000 in a term deposit paying 3.8% per annum simple interest for 2 years. Find the interest earned and the total amount at maturity.
Step 1, Spot the rule.
Principal, rate per annum, time in years → simple interest formula I = P × R × T.
Reason: simple interest is calculated only on the original principal each year, never on the running balance.
Step 2, Identify the three variables.
P = $5,000 R = 3.8% T = 2 years
Reason: write what we know explicitly so we don't lose track during the calculation.
Step 3, Convert the rate to a decimal.
R = 3.8 ÷ 100 = 0.038
Reason: the formula expects R as a decimal, using 3.8 directly would make the answer 100× too big.
Step 4, Substitute into I = P × R × T.
I = 5,000 × 0.038 × 2 = 380
Reason: just three multiplications. 5,000 × 0.038 = 190 per year, × 2 years = $380.
Step 5, Find the total amount A = P + I.
A = 5,000 + 380 = 5,380
Reason: at maturity the investor receives the principal back plus all the interest earned.
Answer: Interest earned = $380; total amount at maturity = $5,380.
2. We do, fill in the missing steps
Same structure as Section 1, but with the working faded. Fill in each blank. 4 marks
Problem. A business borrows $12,000 at 6.5% p.a. simple interest. The total interest paid is $390. Find the duration of the loan in months.
Step 1, Spot the rule: we know I, P and R; we need T. Rearrange I = PRT to ____ = I ÷ (P × R).
Step 2, Identify and convert.
P = $______ R = ______% = ______ I = $______
Step 3, Compute P × R:
P × R = ______ × ______ = ______
Step 4, Solve for T (in years):
T = $390 ÷ ______ = ______ years
Step 5, Convert to months:
______ years × 12 = ______ months
3. You do, independent practice
Show your working in the space under each problem. The first four are foundation (single rule). The middle two are standard (two-step). The last two are extension (multi-step including time conversions or rearrangement).
Foundation, single rule
3.1 Find the simple interest on $4,000 at 6% p.a. for 3 years. 1 mark
3.2 Find the simple interest on $5,000 at 4% p.a. for 2 years. 1 mark
3.3 Convert 6 months and 18 months into years (as decimals). 1 mark
3.4 Find the total amount when $2,000 is invested at 5% p.a. simple interest for 4 years. 1 mark
Standard, two steps
3.5 Calculate the simple interest on $8,000 invested at 5.5% p.a. for 4 years. 2 marks
3.6 A loan of $3,500 attracts simple interest at 8% p.a. How much interest is paid after 9 months? 2 marks
Extension, push your thinking
3.7 An investment earns $450 in simple interest over 2.5 years at 3% p.a. Find the principal. 2 marks
3.8 Maya invests $7,500 for 18 months and earns $506.25 in simple interest. Find the annual interest rate. 3 marks
Section 2, We do (faded business loan)
Step 1: T = I ÷ (P × R).
Step 2: P = $12,000; R = 6.5% = 0.065; I = $390.
Step 3: P × R = 12,000 × 0.065 = 780.
Step 4: T = $390 ÷ 780 = 0.5 years.
Step 5: 0.5 × 12 = 6 months. The loan was for 6 months.
3.1, Simple interest on $4,000 at 6% × 3
I = 4,000 × 0.06 × 3 = $720.
3.2, Simple interest on $5,000 at 4% × 2
I = 5,000 × 0.04 × 2 = $400.
3.3, Time conversions
6 months = 6 ÷ 12 = 0.5 years. 18 months = 18 ÷ 12 = 1.5 years.
3.4, Total amount
I = 2,000 × 0.05 × 4 = $400.
A = $2,000 + $400 = $2,400.
3.5, $8,000 at 5.5% × 4
R = 0.055. I = 8,000 × 0.055 × 4 = 440 × 4 = $1,760.
3.6-9-month loan
T = 9 ÷ 12 = 0.75 years.
I = 3,500 × 0.08 × 0.75 = 280 × 0.75 = $210.
3.7, Find the principal
From I = PRT: P = I ÷ (R × T) = 450 ÷ (0.03 × 2.5) = 450 ÷ 0.075 = $6,000.
3.8, Find the rate
T = 18 ÷ 12 = 1.5 years. P × T = 7,500 × 1.5 = 11,250.
R = I ÷ (P × T) = 506.25 ÷ 11,250 = 0.045 = 4.5% p.a.
Check: 7,500 × 0.045 × 1.5 = 337.50 × 1.5 = $506.25 ✓.