Money and Financial Maths

Money questions use the maths you already know (adding, subtracting, multiplying and dividing) in everyday situations: shopping and change, wages, bills, budgets, profit and loss, VAT and paying for something in instalments.

In the exam you are usually asked to work out an amount of money, such as a total cost, the change, someone's pay or a monthly payment, for 2 to 5 marks. Some questions ask you to decide which option is cheaper, or whether someone made a profit or a loss, and show the figures that prove it.

Most money questions take two or three steps. Read the question carefully, write down each step with a label, such as "cost of pens", and check at the end that your answer is a sensible amount.

There are 100 pence in £1. So 85p is £0.85, 7p is £0.07 and 250p is £2.50. To change pence to pounds, divide by 100

Use one unit all the way through a calculation. If some prices are in pence and some in pounds, change the pence to pounds first, then work in pounds.

Write an amount in pounds with 2 decimal places. If your calculator shows 10.6, write £10.60, not £10.6 or £10.06. Don't write £ and p together: £0.45 or 45p, never £0.45p.

Change is the money you get back: the amount you hand over minus the total cost. A budget is the most you can spend. Add up everything that is spent, then subtract the total from the budget to find what is left.

When someone is paid by the hour, multiply the number of hours by the rate of pay, the amount paid for each hour.

\text{pay} = \text{hours worked} \times \text{rate of pay per hour}

For example, 20 hours at £9.50 per hour is 20 \times \pounds 9.50 = \pounds 190

Overtime is extra hours, often paid at a higher rate, such as 1.5 times the normal rate. Split the hours into two groups: the normal hours at the normal rate, and the extra hours at the higher rate. Work out each group's pay, then add.

Some people also get a bonus of a percentage of their sales. A bonus of 5\% of £20 000 is \pounds 20\,000 \div 100 \times 5 = \pounds 1000. Add it to the basic pay to find the total pay.

Gas and electricity are charged by the unit, often the kWh. The units used are the difference between two meter readings: the later reading minus the earlier one.

Many bills also have a fixed charge for each day, which is paid however much is used. So the bill has two parts.

\text{bill} = \text{days} \times \text{charge per day} + \text{units used} \times \text{price per unit}

To decide which deal is cheaper, work out the total cost of each deal for the same amount, then compare. Write down both totals in your answer, so the examiner can see why you chose one.

The cost is what is paid out, for example to buy or make things. The money taken is what comes in from selling them. If more comes in than was paid out, the difference is a profit. If less comes in, the difference is a loss.

\text{profit} = \text{money taken} - \text{cost}

For example, a car bought for £3000 and sold for £2600 makes a loss of £400.

Percentage profit compares the profit with the cost, which is what was paid at the start. Divide the profit by the cost, not by the money taken, then multiply by 100

\text{percentage profit} = \frac{\text{profit}}{\text{cost}} \times 100

VAT is a tax added to the price of many things. The question tells you the rate, usually 20\%. Work out 20\% of the price and add it on. For £60: 10\% is £6, so 20\% is £12, and the price with VAT is £72.

Other costs can go up or down by a percentage in the same way. If a phone contract costs £30 a month and goes up by 5\%: 10\% is £3, so 5\% is £1.50, and the new cost is £31.50. If the cost goes down, subtract instead.

To pay in instalments, you often pay a deposit first and then the rest in equal payments, usually monthly. Take the deposit away from the total cost before you divide.

\text{each payment} = (\text{total cost} - \text{deposit}) \div \text{number of payments}

• Mixing pounds and pence. Change everything to pounds (or everything to pence) before you calculate, and give the answer in the units asked for.
• Putting the decimal point in the wrong place. Check the size of your answer: 736p is £7.36, not £736 or £73.60.
• Missing a step in a longer question. List every step before you start: take off the deposit before dividing, add the fixed charge, and subtract the earlier meter reading.
• Dividing by the wrong amount for percentage profit. Divide the profit by the cost, which is what was paid at the start, not by the money taken.
• Giving the profit when the question asks for the percentage profit. A profit of £2 on a cost of £10 is a 20\% profit, not a 2\% profit.
• Leaving an answer that is not sensible. A monthly bill of thousands of pounds, or a price that does not give enough money, means something has gone wrong, so check your working.