Topic Review — Financial Mathematics — Solutions

Click any answer to watch the solution video.

1. Percentage increases, decreases, and reverses

   1. Increase $480 by 15%: $480 × 1.15 = $552
   2. Decrease $750 by 20%: $750 × 0.80 = $600
   3. After 25% increase, price is $375: Original = $375 ÷ 1.25 = $300
   4. Jacket $136 after 15% discount: Original = $136 ÷ 0.85 = $160
   5. Laptop $1650 incl. GST: Pre-GST = $1650 ÷ 1.10 = $1500. GST = $1650 − $1500 = $150

2. Simple interest calculations

   1. P=$5000, R=6%, T=3 yr: I = 5000×6×3÷100 = $900
   2. P=$3500, R=4%, T=4 yr total amount: I = 3500×4×4÷100 = $560. A = $3500 + $560 = $4060
   3. R: I=$720, P=$4000, T=3 yr: R = 720×100÷(4000×3) = 72 000÷12 000 = 6% p.a.
   4. T: I=$1050, P=$7000, R=5%: T = 1050×100÷(7000×5) = 105 000÷35 000 = 3 years
   5. P: I=$540, R=4.5%, T=4 yr: P = 540×100÷(4.5×4) = 54 000÷18 = $3000

3. Compound interest and depreciation

   1. P=$4000, r=5%, n=3: A = 4000×(1.05)³ = 4000×1.157625 = $4630.50
   2. P=$9000, r=3.5%, n=4: A = 9000×(1.035)&sup4; = 9000×1.147523 = $10 327.71
   3. CI earned: P=$6000, r=4%, n=5: A = 6000×(1.04)&sup5; = 6000×1.216653 = $7299.92. CI = $7299.92 − $6000 = $1299.92
   4. Motorbike $12 000, 14% p.a., 4 yr: A = 12 000×(0.86)&sup4; = 12 000×0.54700 = $6564.05
   5. Computer $3500, 25% p.a., 3 yr: A = 3500×(0.75)³ = 3500×0.421875 = $1476.56

4. Multi-step financial problems

   1. +10% then −10% on $400: $400×1.10 = $440. $440×0.90 = $396. Not the same — the decrease removes 10% of the larger amount. Net result = 99% of original.
   2. $8000 at 5%, 4 yr, SI vs CI: SI: I = 8000×5×4÷100 = $1600. Total = $9600. CI: A = 8000×(1.05)&sup4; = 8000×1.215506 = $9724.05. CI earns $124.05 more.
   3. Tradesperson $680 + GST, student pays from $750: Total bill = $680×1.10 = $748. Change = $750 − $748 = $2
   4. Agent 2.5% commission, earns $3750: Total sales = $3750 ÷ 0.025 = $150 000
   5. 50 items at $24, 45 sold at $36, 5 at 50% off: Cost = 50×$24 = $1200. Revenue: 45×$36 = $1620 + 5×$18 = $90 = $1710. Profit = $1710−$1200 = $510. Profit% = (510/1200)×100 = 42.5%

5. Problem solving — choosing the right financial tool

   1. $20 000 for 5 yr, Options A/B/C: A (7% SI): I = 20000×7×5÷100 = $7000. Total = $27 000. B (6% CI): A = 20000×(1.06)&sup5; = 20000×1.338226 = $26 764.51. C (5.5% CI): A = 20000×(1.055)&sup5; = 20000×1.306960 = $26 139.21. Rank: A > B > C
   2. Car $38 000, 15% p.a. depreciation for 5 yr: A = 38 000×(0.85)&sup5; = 38 000×0.443705 = $16 860.79. Actual value after 5 yr = $16 860.79. Loss = $38 000 − $16 860.79 = $21 139.21. % loss = (21 139.21/38 000)×100 ≈ 55.6%. The buyer’s claim of 75% loss is incorrect.
   3. Home loan $350 000, 4.8% SI, 20 yr:
      1. I = 350 000×4.8×20÷100 = $336 000. Total = $350 000 + $336 000 = $686 000
      2. Monthly = $686 000 ÷ 240 = $2858.33 per month
      3. Simple interest is rarely used for mortgages. In practice, compound interest is applied (usually monthly), meaning each payment covers accumulated interest first. The total repayment under compound interest would be significantly higher than $686 000, as interest compounds on the outstanding balance each period.