$20,000 at 2% a year, compounded yearly: the amount after 1 year is $□, after 2 years $□, after 3 years $□. Fill in each blank

20,400, 20,808, 21,224.16. Times 1.02 each year: 20000 × 1.02 = 20400, 20400 × 1.02 = 20808, 20808 × 1.02 = 21224.16. Or in one step: 20000 × 1.02^3 = 21224.16.

A triangle's base grows 20% and its height shrinks 10%: its area becomes □ times as much, □% more. Fill in each blank

1.08, 8. Area = base × height ÷ 2, so the factors multiply: (1 + 20%) × (1 − 10%) = 1.08, 8% more.

Net chargeable income is taxed at 2% on the first $50,000, 6% on the next $50,000, 10% on the next $50,000, 14% on the next $50,000 and 17% on the rest. A year's income of $331,000, $10,000 of deductible pension contributions and a $264,000 allowance: salaries tax = $□

1,420. Net chargeable income = 331000 − 10000 − 264000 = 57000; taxed band by band, 1420.

Percentages and ratio · Ages 13–14

Percentages (II)

From “Compound interest” to “Salaries tax”, step by step, each skill with its methods, worked examples and answers.

Skills and methods in this topic, easy to hard

Compound interestA = P × (1 + r%)ⁿ, interest = A − P
Method8000 × 1.05³ = 9261
Another way: Year by year8000 → 8400 → 8820 → 9261
Compounding periodsRate a period = yearly rate ÷ periods a year; periods = years × periods a year
Method10000 × 1.04⁴ = 11698.5856
Another way: Period by period10000 → 10400 → 10816 → 11248.64 → 11698.5856
Growth and depreciationGrowth: times (1 + r%)ⁿ. Depreciation: times (1 − r%)ⁿ
Method200000 × 0.9³ = 145800
Another way: Year by year200000 → 180000 → 162000 → 145800
Changes in the partsParts multiplied: multiply the factors. Parts divided: divide them
Method1.2 × 0.9 = 1.08: the area is up 8%
Another way: Put numbers in12 × 9 = 108, 108 ÷ 100 = 1.08
Chains of sellers and offersEach seller's cost is the last one's price: multiply along
Method100 × 1.2 × 1.25 × 1.4 = 210
Another way: Seller by seller100 → 120 → 150 → 210
Salaries taxAllowances off first, then tax band by band
Method50000 × 2% + 50000 × 6% + 30000 × 10% = 7000
Another way: Top rate, less the savings130000 × 10% − 50000 × 8% − 50000 × 4% = 7000

Worked examples

From different skills in this topic. Have a go first, then open each one for the answer and the working.

Example 1Compound interest →
$20,000 at 2% a year, compounded yearly: the amount after 1 year is $, after 2 years $, after 3 years $.
Fill in each blank
Show the answer and working
Answer: 20,400, 20,808, 21,224.16
Times 1.02 each year: 20000 × 1.02 = 20400, 20400 × 1.02 = 20808, 20808 × 1.02 = 21224.16. Or in one step: 20000 × 1.02³ = 21224.16.
Example 2Changes in the parts →
A triangle's base grows 20% and its height shrinks 10%: its area becomes times as much, % more.
Fill in each blank
Show the answer and working
Answer: 1.08, 8
Area = base × height ÷ 2, so the factors multiply: (1 + 20%) × (1 − 10%) = 1.08, 8% more.
Example 3Salaries tax →
Net chargeable income is taxed at 2% on the first $50,000, 6% on the next $50,000, 10% on the next $50,000, 14% on the next $50,000 and 17% on the rest. A year's income of $331,000, $10,000 of deductible pension contributions and a $264,000 allowance: salaries tax = $
Show the answer and working
Answer: 1,420
Net chargeable income = 331000 − 10000 − 264000 = 57000; taxed band by band, 1420.

Free worksheet: Percentages (II)Working out, multiple choice and word problems, with answers and working, to print or save as a PDF

VIP practice notes and papers

Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.

Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
Practice paper: Set out in parts like a school paper, marked, with answers and full working

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