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Bills, VAT, standing charges, profit and loss, interest, tax, USC, currency exchange and value for money.
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Many household bills have a standing charge (a fixed amount) plus a charge per unit, and then VAT on the total.
An electricity bill is charged as follows:
Find the total amount of the bill.
Cost of units \(= 1320 \times 0.24 = 316.8\) → €316.80.
Total before VAT \(= 28.50 + 316.80 = 345.30\) (euro).
Multiplier for \(13.5\%\) VAT: \(1.135\).
Total bill \(= 345.30 \times 1.135 \approx 391.92\).
Answer: €391.92.
A car hire company charges €70 per day plus 40c per kilometre.
(i) Day charge \(= 6 \times 70 = 420\) → €420.
Distance charge \(= 780 \times 0.40 = 312\) → €312.
Total cost \(= 420 + 312 = 732\) → €732.
(ii) Day charge for 9 days \(= 9 \times 70 = 630\) → €630.
Distance part of bill \(= 945 - 630 = 315\) → €315.
Distance \(= 315 \div 0.40 = 787.5\) km (about \(788\) km).
Answer: Aisling drove about \(788\) km.
A gas bill has a standing charge of €25 and 900 units at 20c per unit. Before VAT is added, the cost is:
Shops compare prices using profit, mark-up and margin.
A shop buys a hoodie for €32 and sells it for €45.
Profit \(= 45 - 32 = 13\) → €13.
Mark-up \(= \dfrac{13}{32} \times 100\% \approx 40.6\%\).
Answer: profit €13, mark-up ≈ \(40.6\%\).
A shop buys trainers for €60 and sells them for €75.
Profit \(= 75 - 60 = 15\) → €15.
Mark-up \(= \dfrac{15}{60}\times 100\% = 25\%\).
Margin \(= \dfrac{15}{75}\times 100\% = 20\%\).
Answer: mark-up \(25\%\), margin \(20\%\) (mark-up is larger).
A laptop costs a shop €500 and is sold for €620. What is the mark-up (percentage profit on cost price), correct to the nearest whole percent?
Interest is money earned on savings or charged on a loan.
Sarah invests €500 at 4% compound interest per year. Find the value of her investment after 3 years, correct to the nearest cent.
Multiplier \(= 1 + 0.04 = 1.04\).
After 3 years: \(500 \times 1.04^3 \approx 500 \times 1.12432 = 562.16\).
Answer: about €562.16.
A sum of money is invested at \(6\%\) simple interest per annum. At the end of one year it amounts to €8480. Find the sum invested.
Amount after 1 year \(= P(1+0.06)\).
So \(P = \dfrac{8480}{1.06} = 8000\).
Answer: €8000 was invested.
€2500 was invested at simple interest for one year and amounted to €2637.50. Find the rate of interest.
Interest earned \(= 2637.50 - 2500 = 137.5\).
Rate \(= \dfrac{137.5}{2500} \times 100\% = 5.5\%\).
Answer: \(5.5\%\) per annum.
A machine costs €15 000 and depreciates by \(15\%\) per annum. Find its value at the end of two years.
Multiplier for a \(15\%\) decrease is \(1 - 0.15 = 0.85\).
Value after 2 years \(= 15000 \times 0.85^2 = 15000 \times 0.7225 = 10837.5\).
Answer: €10 837.50.
Gross pay is total pay before any deductions. Net pay is what is left after all deductions.
Income tax is calculated first, then tax credits are subtracted: \[ \text{income tax payable} = \text{gross tax} - \text{tax credits}. \]
Conor has a monthly wage of €3400. The standard rate of income tax is \(20\%\) and his monthly tax credit is €280. Find how much income tax he pays each month.
Gross tax \(= 0.20 \times 3400 = 680\) → €680.
Tax payable \(= 680 - 280 = 400\) → €400.
Answer: Conor pays €400 per month.
Aoife has an annual salary of €46 000. Her standard rate cut-off point is €36 800 and her tax credit is €3100. The standard rate is \(20\%\) and the higher rate is \(40\%\).
Tax at \(20\%\) on first €36 800: \(0.20 \times 36800 = 7360\) → €7360.
Remaining income \(= 46000 - 36800 = 9200\).
Tax at \(40\%\): \(0.40 \times 9200 = 3680\) → €3680.
Gross tax \(= 7360 + 3680 = 11040\) → €11 040.
Tax payable \(= 11040 - 3100 = 7940\) → €7940.
Answer: gross tax €11 040, tax paid €7940.
Use the following USC rates:
| Band | Income range (per year) | Rate of USC |
|---|---|---|
| 1 | €0 – €12 000 | 0.5% |
| 2 | €12 000 – €20 000 | 2% |
| 3 | €20 000 – €70 000 | 4.5% |
| 4 | Over €70 000 | 8% |
Niamh has an annual salary of €57 000. Calculate her USC for the year.
Band 1: first €12 000 at \(0.5\%\): \(12000 \times 0.005 = 60\) → €60.
Band 2: next €8000 at \(2\%\): \(8000 \times 0.02 = 160\) → €160.
Band 3: remaining \(= 57000 - 20000 = 37000\) at \(4.5\%\): \(37000 \times 0.045 = 1665\) → €1665.
Total USC \(= 60 + 160 + 1665 = 1885\) → €1885.
Answer: USC for the year is €1885.
Which statement is true?
Exchange questions always come from the rate. Example: if \(1\text{ euro} = 1.5\) Canadian dollars (CAD) then:
Suppose \(1\text{ euro} = 1.5\) Canadian dollars (CAD).
(i) \(2800 \times 1.5 = 4200\) → 4200 CAD.
(ii) \(4350 \div 1.5 = 2900\) → €2900.
Answer: 4200 CAD and €2900.
A visitor exchanges 4200 Swiss francs (CHF) for euro. The rate is \(1\text{ euro} = 1.4\) CHF. The bureau charges \(1\%\) commission on the euro received. Find, in euro, what the visitor receives.
First convert without commission: \(4200 \div 1.4 = 3000\) → €3000.
Commission \(= 0.01 \times 3000 = 30\) → €30.
Euro received \(= 3000 - 30 = 2970\) → €2970.
Answer: €2970.
To compare offers fairly, compare the price per unit (for example, price per kilogram or per litre).
Drink A: six 330 ml cans for €4.50. Drink B: four 500 ml bottles for €4.80. Which is better value for money?
Total volume of A: \(6 \times 0.33 = 1.98\) litres.
Price per litre for A: \(4.50 \div 1.98 \approx 2.27\) → about €2.27.
Total volume of B: \(4 \times 0.50 = 2\) litres.
Price per litre for B: \(4.80 \div 2 = 2.40\) → €2.40.
Answer: Drink A is slightly better value.
Which is better value: Option 1 – 750 g for €3.45, or Option 2 – 1 kg for €4.40?
