# A Bit of Everyday Maths

## Maths helps you navigate our world.

Numbers are everywhere. Maths is all around us. A basic understanding of mathematics is important for the decisions we make in our lives. This article gives a few examples of everyday mathematics.

# The maths of shopping

How do you know when you have found a bargain? We want to constrain how much we spend and get a good deal.

Supermarket labels will now often show the price per unit or set amount. For example, liquids might have their price per litre shown.

However, you may need to calculate this figure yourself. Supermarkets can be inconsistent too.

Imagine you are buying dishwasher tablets. There are two products:

- £9 for 65 tabs, weighing 878g (which is a reduced price);
- £6 for 46 tabs, weighing 736g (and not on offer).

The second product is *slightly* cheaper per tab. It is 13p per tab versus 14p for the ‘offer’ product.

There is a larger difference in terms of weight: a kilogram of the second product is priced at £8.15. The ‘offer’ product is priced at £10.25 per kilogram.

Despite being on offer, that product is more expensive.

# The maths of baking

When baking, it is the *ratio* of ingredients that matters. A standard recipe for 12 vanilla cupcakes is:

- 150g margarine;
- 150g caster sugar;
- 150g self-raising flour;
- 3 eggs.

(Half a teaspoon of baking powder can boost the cakes. Vanilla bean paste is also great for flavour.)

Since a large egg weighs around 50g, this means vanilla cupcakes are: one part margarine, one part caster sugar, one part self-raising flour, and one part egg.

This ratio of ingredients is written as 1:1:1:1. The resulting mixture is 600g.

If we wanted to make 24 cupcakes, we need to multiple all those ingredients for 12 cupcakes by two. We would need six eggs and 300g each of the other ingredients.

# The maths of mortgages

A mortgage is a loan to buy a house. The mortgage lender can take possession of the property if repayments are not upheld.

Like other loans, mortgages charge interest — a relative interest in the total debt. Banking institutions make money by charging more interest for mortgages than they do for savings.

Take a mortgage of £250,000, which we will initially seek to repay over 20 years. That mortgage is charged 3.5% interest. Interest rates are often expressed annually, but charged monthly.

At the start of the mortgage, there is a debt of £250,000. Interest is then charged. 3.5% divided by 12 is about 0.29%. That percentage of £250,000 is around £729. Monthly repayments go towards paying off the mortgage interest, and then reducing that initial £250,000.

In this mortgage, we are repaying £1,450 for 240 months (20 years). Over that time, the banking institution charges interest of £97,976. The total mortgage cost is £347,976 (the initial value plus total interest).

**How does a person reduce that interest? **By overpaying. I look at three scenarios for overpaying:

- Overpaying £10,000 in the 12th month;
- Overpaying £200 each month, from the 12th month to the 61st month;
- Overpaying £10,000 in the 60th month.

Each scenario involves overpaying by £10,000, or 4% of the original mortgage value. Relative to making no over-payments, these three scenarios save in interest: £9,084, £7,808, and £6,635 respectively.

If you can, it is better to chip away with smaller over-payments, rather than wait to make a big cut in the mortgage debt. This is because you reduce the total debt earlier, meaning you get charged less interest.