Household Finance

Money problems use familiar operations

Household finance questions put addition, subtraction, multiplication and division into situations involving prices, earnings and bank accounts. First decide what each amount represents. The same subtraction can describe a profit, a loss, tax taken from pay or money leaving an account; the context tells you what the answer means.

Buying and selling: profit or loss

A cost price is what an item costs to buy or make; its selling price is what someone receives for it. If the selling price is higher, the difference is a profit. If it is lower, the difference is a loss:

$\text{profit}=\text{selling price}-\text{cost price}$

$\text{loss}=\text{cost price}-\text{selling price}$

For example, an item bought for £18 and sold for £23 makes a £5 profit. Sold for £15 instead, it makes a £3 loss. In each case the difference is positive; the word profit or loss explains which price was greater. If a question gives the cost and profit, add them to find the selling price. If it gives the cost and loss, subtract the loss.

Reading money into and out of an account

On a bank statement, a credit is money coming into the account, such as pay. A debit is money going out, such as a bill or a card payment. The balance is the running amount in the account. To update it, add credits and subtract debits:

$\text{new balance}=\text{previous balance}+\text{credits}-\text{debits}$

Suppose the balance is £120. A £35 debit leaves £85; a later £50 credit raises it to £135. Following transactions in order matters when a question asks for the balance at a particular point. In a household budget, income is money received and expenditure is money spent, so the same add-and-subtract reasoning shows what remains.

Tax on earnings and purchases

Income tax is tax paid on taxable income, such as earnings. If a question gives gross pay and the income tax deducted, subtract the tax to find the pay remaining after that deduction. For instance, £800 gross pay less £90 income tax leaves £710. Other deductions may also be stated, so do not treat this as final take-home pay unless the question allows it.

VAT, or value added tax, is included in the price of many goods and services. When a price is given before VAT, calculate the VAT from that price and add it. For example, at a rate of 20%, a £30 price before VAT has £6 VAT, making £36 including VAT. Rates can differ, so use the rate and price basis stated in the question. A price already described as including VAT must not have VAT added again.

Interest on savings and borrowing

Interest is money added to savings or charged for borrowing. An interest rate tells you the percentage for a stated period, commonly a year. For one period, apply the stated percentage to the amount on which interest is being calculated. If £200 earns 3% interest for one year, the interest is £6 and the new balance is £206. If the same £6 were a charge on a loan, it would increase what is owed instead. For problems covering more than one period, read carefully whether interest is calculated on the original amount or on an updated balance.

Prices

Selling price above cost price: $\text{profit}=\text{selling price}-\text{cost price}$. Selling price below cost price: $\text{loss}=\text{cost price}-\text{selling price}$.

Accounts

For a bank account, credit adds and debit subtracts: $\text{new balance}=\text{old balance}+\text{credits}-\text{debits}$.

Tax and interest

Income tax reduces earnings. VAT is included in the final price: if starting with a price before VAT, calculate and add the stated tax. Interest is a percentage of the relevant savings or borrowing amount for a stated period; check which amount and period the question specifies.