教育者の方へ： Percentage change, interest and growth or decay（Mathematics、Ratio, proportion and rates of change）向けのすぐ使えるレッスンスライド, 復習ノート — レッスンで使うか、学習者がライブゲームとして遊ぶインタラクティブなクラス活動としてトピックを実施できます。
Percentage change = \frac{\text{change}}{\text{original}} \times 100. A price rising from £40 to £46 is \frac{6}{40} \times 100 = 15\% increase.
Use multipliers: increase by 15% → ×1.15; decrease by 20% → ×0.8. Multiplier = 1 ± (percentage as a decimal).
Reverse percentages
To find the original, divide by the multiplier. A coat is £68 after a 15% reduction: 68 \div 0.85 = £80.
Do not just add 15% to the new price.
Simple and compound interest
With unchanged principal P, fixed annual percentage rate R and time T in years, simple interest is PRT/100. £500 at 4% for 3 years earns £60.
For annual compound interest A = P(1 + r)ⁿ, r is the annual decimal rate and n is whole years. £500 × 1.04³ ≈ £562.43.
Same £500 principal and 4% annual rate
Growth and decay
Exponential growth/decay uses the same multiplier idea: a population growing at 5% a year multiplies by 1.05 each year; depreciation of 12% a year multiplies by 0.88.
After n periods: final = original × multipliern.
Repeated percentage changes
Multiply the multipliers: +10% then −10% is 1.1 \times 0.9 = 0.99, an overall 1% decrease, not no change.
スライド
Sign up free to view the lesson slides
Step through every slide for this topic — plus flashcards and revision notes — with a free account.
4.A TV costs £400 and is reduced by 15% in a sale. What is the sale price?
Easy
A£340
B£60
C£385
D£460
5.A price rises from £40 to £46. What is the percentage increase?
Easy
A6%
B15%
C13%
D86%
6.A value falls from £250 to £200. What is the percentage decrease?
Easy
A20%
B25%
C50%
D80%
7.£500 is invested at 4% simple interest for 3 years. How much interest is earned?
Easy
A£60
B£62.43
C£20
D£120
8.A coat costs £68 after a 15% reduction. What was the original price?
Medium
A£80
B£78.20
C£58
D£85
もっと問題
9.After a 20% increase a rent is £600. What was the original rent?
Medium
A£480
B£500
C£720
D£520
10.£500 is invested at 4% compound interest for 3 years. What is the final amount (nearest penny)?
Medium
A£562.43
B£560.00
C£600.00
D£562.00
11.A car worth £12 000 depreciates at 15% a year. What is it worth after 2 years?
Medium
A£8 670
B£8 400
C£9 000
D£10 200
12.A population of 2000 grows by 5% a year. What is it after 3 years (nearest whole)?
Medium
A2315
B2300
C2400
D2100
13.Increase £200 by 10% and then decrease the result by 10%. What is the final amount?
Medium
A£200
B£198
C£202
D£220
14.What is the single multiplier for +10% then −10%?
Medium
A1
B0.99
C1.01
D0.9
15.In one week a price is reduced by 10% and the next by 20%. What is the single multiplier?
Medium
A0.7
B0.72
C0.68
D0.3
16.A sum of £2000 earns compound interest of 3% a year. After how many years does it first exceed £2200?
Medium
A4
B3
C5
D2
17.A house increased in value by 12% to £280 000. What was its value before?
Medium
A£250 000
B£246 400
C£313 600
D£268 000
18.A value decreases by 8% each year. After 5 years it is £6 000. About how much was it originally?
Medium
A£9 100
B£8 400
C£7 200
D£10 000
19.For the same positive principal and no fees or withdrawals, which gives more money after 2 years: 5% annual simple interest or 5% interest compounded annually?
Medium
Acompound
Bsimple
Cequal
Dcannot tell
20.What is 15% as a decimal multiplier for an increase?
Easy
A1.15
B0.15
C0.85
D15
21.What does \frac{\text{change}}{\text{original}} \times 100 calculate?
Easy
Apercentage change
Bpercentage of
Cratio
Dmean
22.A bike costs £120 including 20% VAT. What is the price without VAT?
Medium
A£100
B£96
C£144
D£110
23.Compound interest uses which multiplier for 6% growth?
Easy
A1.06
B0.06
C0.94
D6
24.The multiplier for a 30% decrease is 0.7.
Easy
True or false?
25.A 10% increase followed by a 10% decrease leaves a value unchanged.
Easy
True or false?
26.A reverse percentage problem with a nonzero multiplier is solved by dividing the new value by that multiplier.
Easy
True or false?
27.At a fixed annual simple-interest rate on an unchanged original principal, the interest added each year is the same.
Easy
True or false?
28.Compound interest on £100 at 10% for 2 years gives £120.
Medium
True or false?
29.Which multipliers are correct?
Medium
A20% increase: 1.2
B20% decrease: 0.8
C5% increase: 1.5
D5% decrease: 0.95
E12% increase: 1.012
30.Which give £121 from £100?
Medium
A10% compound for 2 years
B10% simple for 2 years
C100 \times 1.1 \times 1.1
D100 \times 1.21
E100 \times 1.2
31.A car costs £15 000 and loses 20% of its value each year. Calculate its value after 3 years.
