Working with money: Budgets, savings, discount, interest and exchange rates

1.7 Working with money: Budgets, savings, discount, interest and exchange rates

In business and in everyday life, we use money to pay for services and goods. There are different financial models, and it is useful to understand how the prices are set. It is also important to save money and budget for different expenses.

Budgets and savings

A budget is a plan about how you will spend, and save, your money. Budgets are a very important part of planning for a sound financial future.

You can include saving money in your budget. Think of what you want to save money for and work out how long it will take you. For example, if your goal is to save \(\text{R} 200\) in \(10\) months, you would need to save \(\text{R} 20\) every month. You could also keep track of different amounts you save to make sure you still have \(\text{R} 200\) at the end of the \(10^{\text{th}}\) month.

temp text

Profit and loss

When people start a business, they need to be able to work with cash flows and monitor their sales. There are different costs involved to make the sales. These costs are needed to perform business. For example, to make clothes you need to buy fabric, a sewing machine, needles, and threads. These are costs, and when you want to sell clothes you made, you will factor these costs in so you can make a profit.

profit

the amount by which the selling price exceeds the costs: profit = selling price – cost price

When the money you get exceeds the expenses or the initial costs, then you make a profit. If you make less money then you spend, then you make a loss.

loss

an amount by which the costs exceed the selling price: loss = cost price – selling price

temp text

Discount

The amount for which a dealer buys an article from a producer or manufacturer is called the cost price. The price marked on the article is called the marked price and the price of the article after mark-up and/or a discount is the selling price.

cost price

the amount for which someone buys something from a producer

discount

an amount that is subtracted from the marked price to determine the selling price

selling price

the amount for which a buyer buys a product; this amount includes the seller’s mark-up and may also include a discount

For example, we can look at this scenario and try to understand the problem.

Rashid is a furniture dealer. He buys a couch for \(\text{R} 2\ 420\). He displays the couch in his showroom with the price marked as \(\text{R} 3\ 200\). Rashid offers a discount of \(\text{R} 320\) to customers who pay cash.

• The cost price of the couch in Rashid’s furniture shop is \(\text{R} 2\ 420\). This is the amount he paid for it.
• The marked price of the couch is \(\text{R} 3\ 200\). This is the amount that is displayed on the couch in his showroom.
• The selling price for a customer who pays cash is \(\text{R} 3\ 200 − \text{R} 320 = \text{R} 2\ 880\). The cash payment attracts a discount of \(\text{R} 320\), meaning that the customer will pay less.

The discount on an article is always less than the marked price of the article. In fact, it is only a fraction of the marked price. The discount of \(\text{R} 320\) that Rashid offers on the couch is \(10\) hundredths of the marked price.

Another word for hundredths is percentage, and the symbol for percentage is \(\%\). So, we can say that Rashid offers a discount of \(10\%\).

For example, \(18\%\) is \(18\) hundredths, and \(25\%\) is \(25\) hundredths.

percentage

a value of hundredths

\(\%\) is a symbol for hundredths. \(8\%\) means \(8\) hundredths and \(15%\) means \(15\) hundredths.

The symbol \(\%\) is just another way of writing the common fraction notation for hundredths.

\(8\%\) is \(\frac{8}{100}\).

A discount of \(6\%\) on an article can be calculated in two steps:

1. Calculate \(1\) hundredth of the marked price (divide by \(100\)).
2. Calculate \(6\) hundredths of the marked price (multiply by \(6\)).

temp text

Interest

When a person borrows money from a bank or some other institution, they normally have to pay for the use of the money. This is called interest. The bank charges the interest on the borrowed amount.

interest

the amount that is paid at a given rate for the use of money that is lent

For example, let’s look at this scenario and try to understand the problem.

Lebo borrows \(\text{R} 7\ 000\) from a bank at \(14\%\) interest for one year. How much does she have to pay back to the bank at the end of the period?

• The amount borrowed is \(\text{R} 7\ 000\).
• The bank charges \(14\%\) interest.

One way to solve this problem is to:

1. calculate the \(\%\) interest
2. add the interest to the original amount to find the total.

So, \(7\ 000 \div 100 = 70\) and \(70 \times 14 = 980\). The amount of interest is \(\text{R} 980\).

Now, add the interest to the amount borrowed. \(7\ 000 + 980 = 7\ 980\).

The total that Lebo needs to pay back to the bank is \(\text{R} 7\ 980\).

temp text

VAT calculations

Value added tax (VAT) is an amount added to the price of goods. VAT goes to the government to spend on services for the citizens of the country. In South Africa, when you see a price in the shops, VAT has usually already been added.

The price including VAT is calculated by adding \(15\%\) to the original price (excluding VAT). Adding \(15\%\) VAT means that we have to pay \(100\% + 15\% = 115\%\) of the original price. This is the same as multiplying by \(115\%\).

When you only know the price including VAT, you need to work backwards. To work backwards from the price including VAT to the original price, we must do the inverse operation. Instead of multiplying by \(115\%\), we must divide by \(115\%\).

Working with percentages, keep in mind that \(\%\) is ‘out of \(100\)’, so remember to divide by \(100\):

\[115\% = \frac{115}{100} = \text{1,15}\]

temp text

Hire purchase

A hire purchase agreement is a credit agreement between a buyer and a financial institution. If the buyer does not have enough money upfront to buy something (for example, a laptop or a fridge), they can choose to make use of a hire purchase agreement instead. They then pay an agreed amount in monthly payments. The item does not belong to them until the final payment is made.

To calculate the amount owed on a hire purchase agreement:

1. Calculate the balance owed on the cash price: balance = cash price − deposit.
2. Calculate the total interest on the balance owed, using simple interest.
3. Total amount owed = balance + total interest.

Hire purchase agreements always use simple interest to calculate monthly repayments. Simple interest means that interest is calculated on the original amount in each year. So, the amount of interest charged is the same in each year.

temp text

Exchange rates

Different countries use different currencies, which is another name for money. Currency is something that we use to exchange for food, clothes, and services. When you travel to another country or read news about that country, you will often need to understand the relationship between the country’s currency and the South African rand. This is called the exchange rate.

exchange rate

the amount of rand that we pay to get another currency.

In South Africa, we use the rand (\(\text{R}\)). In Botswana, for example, they use the pula (\(\text{P}\)). If you go to Botswana and want to buy something there, you have to exchange rand for pula.

temp text