Financial Maths

Profit, Loss, Mark-up, and Margin

Profit is how much more you sell an item for than it cost you, while a loss means it sold for less than it cost:

• Profit = Selling Price − Cost Price
• Loss = Cost Price − Selling Price
• Percentage profit or loss is always calculated on the cost price:

At Higher Level, distinguish carefully between mark-up and margin:

• Mark-up is profit as a percentage of the cost price:

• Margin is profit as a percentage of the selling price:

For example, buy for €40 and sell for €50 (profit €10). The mark-up is $\frac{10}{40} \times 100 = 25\%$, but the margin is $\frac{10}{50} \times 100 = 20\%$.

To find the cost price backwards, treat the selling price as a percentage. A selling price with 25% profit is 125% of cost price, so divide by 1.25.

VAT, Utility Bills, Currency, and Value for Money

VAT is a tax added on to the price of goods and services:

• Adding VAT: multiply the pre-VAT price by $(1 + r)$, where $r$ is the VAT rate as a decimal (e.g. $\times 1.23$ for 23% VAT).
• Taking VAT off: divide the inclusive price by $(1 + r)$ (e.g. €738 including 23% VAT gives $738 \div 1.23 = €600$).

For utility bills, units used = new reading − old reading. Multiply units used by the unit price, add the standing charge, then add VAT.

For a rate written €1 = k units of another currency, multiply euro by k; divide to convert back. Apply commission as the question specifies.

For value for money, find the cost per common unit (e.g. per 100 g or per litre), compare, and write a sentence stating which is better value and why.

Income Tax, Deductions, and Net Pay

Gross income is your total pay before any deductions. Net pay is what you take home after all deductions are removed:

Follow these steps to calculate income tax:

1. Tax income up to the Standard Rate Cut-Off Point at the standard rate (e.g. 20%).
2. Subtract the cut-off point from gross income. Tax this remaining balance at the higher rate (e.g. 40%). If gross income is below the cut-off, tax the entire income at the standard rate.
3. Add the two tax amounts to find gross tax.
4. Subtract tax credits from gross tax; tax payable cannot fall below zero.

Calculate each percentage deduction using the income amount and rate specified. Total deductions include income tax payable and all other deductions given.

Compound Interest and Depreciation

Compound interest adds interest each period to the growing total balance. Depreciation reduces an asset's value by a percentage each year. Both formulae are in the Formulae and Tables booklet:

• Compound interest: $F = P(1 + i)^t$
• Depreciation: $F = P(1 - i)^t$

Here $P$ is the principal or starting value, $i$ is the annual rate as a decimal, $t$ is time in years, and $F$ is the final value.

To find total interest earned, subtract the principal: $\text{Interest} = F - P$.

If the interest rate changes from year to year, or if money is added or withdrawn, do not use the power formula; calculate the balance year by year instead.

Key terms

Standard Rate Cut-Off Point

The maximum amount of income taxed at the standard rate; any income above this is taxed at the higher rate.

Tax Credit

A sum that is subtracted directly from gross tax to determine the income tax payable; tax payable cannot fall below zero.

Gross Tax

The total tax calculated across all tax bands before subtracting tax credits.

Net Pay

Take-home pay left after income tax and all other deductions are subtracted from gross income.

Mark-up

Profit expressed as a percentage of the cost price.

Margin

Profit expressed as a percentage of the selling price.

VAT

Value Added Tax, a government tax added to the price of goods and services.

Standing Charge

A fixed charge on a utility bill that you pay regardless of how much energy or water you use.