Chapter 10 Exercise 10.1 Q. 1.
25,000 × 0.20 = €5,000
Q. 2.
46,000 × 0.225 = 10,350 −2,500 €7,850
Q. 3.
41,500 × 0.22 =
9,130 − 2,340 €6,790
41,500 − 6,790 = €34,710 23,200 × 0.41 =
Q. 4.
9,512
56,000 32,800 × 0.20 = + 6,560 16,072 56,000 − 16,072 = €39,928 Q. 5.
(i)
61,500 × 0.42 = 25,830 94,500 33,000 × 0.21 = + 6,930 32,760 − 3,450 Tax payable 29,310
(ii) 94,500 − 29,310 = €65,190 Q. 6.
37,000 × 0.21 = €7,770 − 2,100 €5,670 Total deductions = 5,670 + 450 + 350 = 6,470 37,000 − 6,470 = €30,530
Q. 7.
(i) 6,300 + 1,300 = 7,600 7,600 (ii) _______ = 0.20 = 20% 38,000
Q. 8.
18,000 × 0.42 =
7,560
50,000 32,000 × 0.20 = + 6,400 13,960 − 3,500 Tax payable €10,460 Active Maths 2 (Strands 1–5): Ch 10 Solutions
1
Q. 9. 10,036 × 0.02 =
200.72
Q. 10. 10,036 × 0.02 =
200.72
5,980 × 0.04 =
239.20
5,980 × 0.04 =
239.20
Q. 11.
18,984 × 0.07 = + 1,328.88
30,484 × 0.07 = + 2,133.88
€1,768.80
€2,573.80
(i)
€127 × 52 = 6,604 65,396 × 0.04 = €2,615.84 €2,615.84 ÷ 52 = €50.30 per week
(ii) 72,000 × 0.1075 = €7,740 7,740 ÷ 52 = €148.85 per week (iii) 10,036 × 0.02 =
200.72
5,980 × 0.04 =
239.20
55,984 × 0.07 = 3,918.88 €4,358.80 (iv)
37,400 × 0.41 = 15,334 72,000 34,600 × 0.20 = + 6,920 €22,254 − 3,000 €19,254 72,000 − 2,615.84 − 4,358.80 −19,254 = 44,771.36 44,771.36 ÷ 52 = €880.22
Q. 12.
(i) 127 × 52 = 6,604 64,000 − 6,604 = 57,396 57,396 × 0.04 = 2,295.84 2,295.84 ÷ 52 = €44.15 per week (ii) 64,000 × 0.1075 = 6,880 6,880 ÷ 52 = €132.31 per week (iii) 10,036 × 0.02 =
200.72
5,980 × 0.04 =
239.20
4,7984 × 0.07 =
3,358.88 €3,798.80
(iv)
31,600 × 0.41 =
12,956
64,000 32,400 × 0.20 = + 6,480 19,436 − 2,400 €17,036 64,000 − 17,036 − 2,295.84 − 3,798.80 = 40,869.36 40,869.36 ÷ 52 = €785.95
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Active Maths 2 (Strands 1–5): Ch 10 Solutions
Q. 13.
(i) 127 × 52 = 6,604;
6,604 × 2 = 13,208
152,000 − 13,208 = 138,792 138,792 × 0.04 = €5,551.68 (ii) 10,036 × 2 = 20,072;
20,072 × 0.02 =
€401.44
5,980 × 2 = 11,960;
11,960 × 0.04 =
€478.40
119,968 × 0.07 = + 8,397.76 €9,277.60 (iii)
86,400 × 0.41 =
35,424
65,600 × 0.20 =
13,120
152,000 48,544 −3,400 €45,144 (iv) 152,000 − 45,144 – 5,551.68 − 9,277.60 − 704 − 5,063 = €86,259.72 Q. 14. 35,400 × 0.20 = 7,080 12,396 − 7,080 = 5,316 5,316 ______ = 12,965.85 0.41 ∴ Gross Income = 35,400 + 12,965.85 = €48,365.85 Q. 15.
(i)
13,000 × 0.41 =
5,330
32,000 × 0.20 =
6,400
45,000 11,730 − 3,800 €7,930 (ii) 13,680 + 3,900 = €17,580 gross tax 32,000 × 0.20 = 6,400 Tax paid at 0.41 = €11,180 11,180 _______ = €27,268.29 0.41 ∴ Gross Income = 32,000 + 27,268.29 = €59,268.29 (iii)
10,036 × 0.02 =
200.72
5,980 × 0.04 =
239.20
43,252.29 × 0.07 = 3,027.66 Total = €3,467.58
Active Maths 2 (Strands 1–5): Ch 10 Solutions
3
Q. 16. (a)
24,700 × 0.41 = 10,127 57,500 32,800 × 0.20 = + 6,560 16,687 − 2,830 13,857 Net Income = 57,500 − 13,857 = €43,643
(b) 15,640 + 2,830 = 18,470 gross tax 18,470 − 6,560 = 11,910 11,910 _______ = 29,048.78 0.41 Gross Income = 29,048.78 + 32,800 = €61,848.78 Q. 17.
(i) 1,650 + 1,650 + 70 = €3,370 (ii)
9,200 × 0.41 = 3,772 42,000 32,800 × 0.20 =
6,560 10,332 − 3,370
Tax Paid €6,962 (iii) 10,036 × 0.02 =
200.72
5,980 × 0.04 =
239.20
25,984 × 0.07 = + 1,818.88 Total USC = €2,258.80 PRSI
€127 × 52 = 6,604 42,000 − 6,604 = 35,396 35,396 × 0.04 = €1,415.84
∴ Net Income = 42,000 − 6,962 − 2,258.80 − 1,415.84 = €31,363.36 17,200 × 0.41 =
Q. 18.
7,052
50,000 32,800 × 0.20 = + 6,560 €13,612 13,612 − 10,460 = €3,152 Q. 19. (a)
13,200 × 0.41 = 5,412 46,000 32,800 × 0.20 = 6,560 11,972 − 2,300 Tax Payable: €9,672
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Active Maths 2 (Strands 1–5): Ch 10 Solutions
(b) €13,680 + 2,900 = €16,580 gross tax 16,580 − 6,560 = €10,020 10,020 _______ = €24,439.02 0.41 Gross Income = €24,439.02 + 32,800 = €57,239.02
Exercise 10.2 Q. 1. (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix) (x)
Q. 2.
Cost price (€)
Selling price (€)
25.00 31.00 15.00 14.00 12.00 18.00 1.00 2.10 10.00 11.00
30.00 36.00 20.00 28.00 18.00 18.90 4.00 2.80 12.00 15.50
Profit (€)
5.00 5.00 5.00 14.00 6.00 0.90 3.00 0.70 2.00 4.50
% Mark-up (2 d.p.) % Margin (2 d.p.)
20.00 16.13 33.33 100.00 50.00 5.00 300.00 33.33 20.00 40.91
16.67 13.89 25.00 60.00 33.33 4.76 75.00 25.00 16.67 29.03
(i) 40 × 0.98 = €39.20 (ii) 85 × 0.95 = €80.75 (iii) 135 × 0.90 = €121.50 (iv) 100 × 0.995 = €99.50 (v) 1,565 × 0.97 = €1,518.05
Q. 3. (a) 18,900 − 16,250 = €2,650 profit 2,650 _______ = 16.31% mark-up 16,250 2,650 (b) _______ = 14.02% margin 18,900 Q. 4. (a) 15,900 − 10,250 = 5,650 5,650 _______ = 55.12% mark-up 10,250 5,650 (b) _______ = 35.53% margin 15,900 Q. 5.
(i) 1,140 × 0.75 = €855 (ii) 855 × 1.15 = €983.25 983.25 − 855 = 128.25 128.25 _______ 983.25
= 13.04%
(i) Company A: 15% mark-up 0.15 ∴ Margin = ____ × 100 1.15 = 13.04% (ii) Company B: 28.6% profit margin
(i) 120 × 1.15 = €138 selling price 18 (ii) ____ = 13% margin 138
Q. 6.
Q. 7.
0.286 mark-up = ______ × 100 0.714 = 40.06% (iii) A company is more likely to advertise it percentage profit mark-up as it is greater than the percentage profit margin and would be more likely to attract investors.
Active Maths 2 (Strands 1–5): Ch 10 Solutions
5
0.33 (iv) 33% margin ⇒ ____ = 49.25% 0.67 I would prefer to buy shares in a company with a 33% profit margin as this is a 49.25% profit on cost price. This is a profit of 6.25% more than the company with percentage profit mark-up of 43%.
Exercise 10.3 Q. 1. F = P(1 +
= €26,046.56
Q. 10. F = P(1 + i)t = 9,600(1 + 0.02)4 = €10,391.35 ∴ Interest = €791.35
Q. 2. F = P(1 + i)t = 16,000(1 + 0.03)6 = €19,104.84
Q. 11. F = P(1 + i)t 2,500 = P(1 + 0.06)5 2,500 ______ =P (1.06)5 €1,868.15 = P
∴ Total Interest = €3,104.84 Q. 3. F = P(1 + i)t = 10,200(1 + 0.034)8 = €13,327.98
Q. 12. F = P(1 + i)t 12,500 = P(1 + 0.032)6 12,500 _______ =P (1.032)6 €10,347.41 = P
Q. 4. F = P(1 + i)t = 1,500,000 (1 + 0.08)3 = €1,889,568 Q. 5. F = P(1 + i)t = 10,000(1 + 0.06)5
Q. 13. F = P(1 + i)t 1,500 = P(1 + 0.035)2 1,500 ______ =P 1.0352 €1,400.27 = P
= €13,382.26 ∴ Interest = €3,382.26 Q. 6. F = P(1 + i)t F = 25,400 (1 + 0.03)10 = €34,135.48 Interest = €34,135.48 − 25,400 = €8,735.48 1,500,000,000 × 1.005
Q. 8. F = P(1 + i)t = 100,500(1 + 0.05)6 = €134,679.61 Q. 9. F = P(1 + i)t = 1,000,000(1.105)3.5 = €1,418,299.58
i)t
= 22,500(1 + 0.05)3
Q. 15.
Q. 7. F = P(1 + i)t = 200,500(1 + 0.025)8 = €244,289.78 Interest = €43,789.78
=
Q. 14. 16,000 × 1.03 = 16,480 − 2,000 14,480 14,480 × 1.02 = €14,769.60
1,507,500,000
1,507,500,000 × 1.0042 = €1,513,831,500 Q. 16.
6
Principal
Rate of interest
Amount at year end
Year 1
€500
2.36%
€511.80
Year 2
€511.80
2.36%
€523.88
Year 3
€523.88
2.36%
€536.24
Active Maths 2 (Strands 1–5): Ch 10 Solutions
Q. 17.
(i) 100,000 × 1.03 = €103,000 (ii) €103,000 − €5,000 = €98,000 98,000(1.0325)3 = €107,868.90 No, the advice is not correct as she will have only €107,868.90 if she invests the remaining €98,000 for the remaining 3 years at 3.25%.
Q. 18.
(i) 1,000 × 0.04 = €40 40 × 3 = €120 1,000 + 120 = €1,120 (ii) This method is incorrect as his interest should be accumulated each year. The correct answer is 1,000(1.04)3 = €1,124.86
Revision Exercises Q. 1.
27,000 × 0.21 = €5,670 −2,100 €3,570 Take-home pay = 27,000 − 3,570 − 450 − 350 = €22,630
Q. 2.
(i) Gross tax = 7,300 + 1,300 = €8,600 8,600 (ii) _______ = 23.24% 37,000
Q. 3.
13,000 × 0.42 =
5,460
32,000 × 0.20 =
6,400 11,860
45,000
−3,500 Tax payable €8,360 Q. 4.
10,036 × 0.02 =
200.72
5,980 × 0.04 =
239.20
19,784 × 0.07 = 1,384.88 Total USC = €1,824.80 7,000 × 0.41 =
Q. 5.
2,870
79,000 72,000 × 0.20 = + 14,400 €17,270 − 3,790 Tax Payable: €13,480
€110 × 12 = €1,320 €240 × 12 = €2,880 €44 × 12 = €528 Total deductions = €18,208 79,000 − 18,208 = €60,792 ÷ 26 = €2,338.15
Active Maths 2 (Strands 1–5): Ch 10 Solutions
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Q. 6. (a) 10,036 × 0.02 =
200.72
5,980 × 0.04 =
239.20
28,984 × 0.07 = 2,028.88 Total USC = €2,468.80 (b) Total tax credits = 1,650 + 1,650 = €3,300 (c) 12,200 × 0.41 = 5,002 45,000 32,800 × 0.20 = 6,560 11,562 − 3,300 Tax Bill: €8,262 (d) 45,000 − 2,468.80 − 8,262 = €34,269.20 Q. 7. (a) 16,000 c.p., 24,000 s.p. 24,000 − 16,000 = €8,000 profit 8,000 _______ 16,000
× 100 = 50% mark-up
8,000 (b) _______ × 100 = 33.33% margin 24,000 Q. 8.
(i) 120 × 1.15 = €138 18 (ii) ____ = 13.04% ≈ 13% margin 138
Q. 9.
(i) 3,750 × 0.75 = €2,812.50 (ii) 2,812.50 × 1.15 = €3,234.38 ∴ Profit = €421.88 421.88 ________ 3,234.38
= 13.04%
Q. 10. (a) By calculating 13.5% of €136.20, Jerry gets a different amount than was originally calculated. 136.20 Price of meal before VAT: _______ = €120 1.135 VAT amount: 13.5% of 120 = €16.20 Jerry’s calculation for the VAT amount: 136.20 × 0.135 = €18.39 (b) 120 × 1.09 = €130.80 Q. 11.
A profit margin of 60% implies that the cost price is 40% of the selling price. To make a profit of 25%: 40% × 1.25 = 50% So, to make a profit of 25%, the manager must sell at 50% of the original selling price. ∴ Prices should be reduced by 50%.
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Active Maths 2 (Strands 1–5): Ch 10 Solutions
Q. 12.
(a) 35,000 × 0.80 = 28,000 28,000 × 0.85 = €23,800 (b) 35,000 − 23,800 = 11,200 11,200 _______ × 100 = 32% fall in value. 35,000 ∴ The manager is incorrect as the actual fall in value is 32%.
Q. 13.
Q. 14.
F = P(1 + i)t
Q. 15. F = P(1 + i)t
= 1,500,000(1 + 0.065)3.5
20,500 = P(1 + 0.05)5
= €1,869,884.95
20,500 _______
=P 1.055 €16,062.29 = P
F = P(1 + i)t = 18600(1 + 0.02)4
Q. 16. F = P(1 + i)t
= €20,133.24
102,500 = P(1 + 0.042)6 102,500 ________ =P 1.0426 €80,078.80 = P
∴ Interest = €1,533.24
Q. 17.
(a) 5,000 × 0.03 = €150 interest Tax: 150 × 0.27 = €40.50 ∴ Interest = €109.50 Amount = €5,109.50 (b) 5,296 − 5,109.50 = €186.50 interest after tax 186.50 ∴ _______ = €255.48 interest before tax 0.73 255.48 ________ × 100 = 5% 5,109.50
Q. 18.
F = P(1 + i)t
Q. 19.
7,290 = P(1.08)2 7,290 ______ =P 1.082 €6,250 = P Q. 20.
(a) $1.58 US = 2.25 Swiss francs 2.25 $1 US = ____ 1.58 $1 = 1.42 Swiss francs. (b) 2.25 Swiss F = $1.58 US 1.58 1 Swiss F = ____ = $0.70 US 2.25
(a) (i) 1,200 × 1.4045 = $1,685.40 (ii) $1,685.40 × 0.97 = $1,634.84 (b) €2,047 after commission is deducted 2,047 ______ = €2,110.31 before commission 0.97 €2,110.31 = $3,060 US 3,060 €1 = ________ 2,110.31 €1 = $1.45 US (c) €1 = £0.89 Active Maths 2 (Strands 1–5): Ch 10 Solutions
9
Q. 21.
(a) 210 m2 = 610 children 610 154 m2 = ____ × 154 210 1 = 447__ children 3 (b) 610 children = 210 24 children =
m2
Combined jugs ⇒ 225 ml : 775 ml orange : water 9 : 31 Q. 25.
(a) John : Paul : Michael 2,250 : 2,600 : 150
210 ____
225 : 260 : 15
× 24 610 = 8.26 m2
Q. 22.
Q. 23.
45 : 52 : 3 150,000 ÷ 100 = €1,500
(i) 4 people = 6 hours
John = 1,500 × 45 = €67,500
6×4 8 people = ______ = 3 hours 8 6×4 ______ (ii) 6 people = = 4 hours 6
Paul = 1,500 × 52 = €78,000 Michael = 1,500 × 3 = €4,500 (b) (i) John : Paul : Michael 2.5 : 1.5 : 1 5 : 3 : 2 ∴ 140,000 = 5 shares
6 people = 300 g 300 8 people = ____ × 8 6 = 400 g of mince
Q. 24.
1 share = €28,000 Total bonus = €280,000
500 ml ÷ 5 = 100 ml 100 ml : 400 ml
(ii) Paul = 28,000 × 3
orange : water
= €84,000
500 ml ÷ 4 = 125 ml 125 ml : 375 ml Q. 26.
Michael = 28,000 × 2
orange : water
= €56,000
€1,200 × 12 = 14,400 €60,000 − €14,400 = €45,600 45,600 _______ = €304,000 is the value of cars he must sell 0.15
Q. 27.
(a) 620 × 12 = €7,440 (b) €7,440 × 0.04 = €297.60 or €24.80 per month (c) 7,440 + 297.60 = €7,737.60 7,737.60 ________ = €644.80 12 (d) 620(1.04)6 = €784.50
Q. 28.
Before:
9 litres = 72 km 1 litre = 8 km
After:
5.5 litres = 58.3 km 58.3 1 litre = ____ 5.5 = 10.6 km
Q. 29.
Increase = 2.6 km
2.6 ___ 8
10
× 100 = 32.5%
Active Maths 2 (Strands 1–5): Ch 10 Solutions
(a) 510 × 0.20 = €102 −63 €39 (b) 193 × 0.02 = 3.86 115 × 0.04 = 4.60 202 × 0.07 = + 14.14 USC €22.60 (c) 76.92 − 39 − 22.60 = €15.32 PRSI
Q. 30.
(i) 2,500 × 1.04 = €2,600
Q. 31.
(i) Fixed charge
2,600 × 1.03 = €2,678 (ii) €2,744.95 − €2,678 = €66.95 66.95 ______ 2,678
Q. 32.
(i)
€15
40 × 0.11
=
€4.40
70 × 0.28
= €19.60 + €39.00
× 100 = 2.5%
(ii) €39 × 1.23 = €47.97
660 × 0.42
= 277.20
240 × 0.20
= + 48
€900 €325.20 −
50 €275.20
(ii) Increase in after-tax weekly income: 58% = €20.30 20.30 Increase in gross weekly income: ______ = €35 0.58
Active Maths 2 (Strands 1–5): Ch 10 Solutions
11
