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Household finance - WJECMortgages

Buying or renting a home can be an expensive task. Thinking about the maths behind household finance now will help you in the future when you move into your own property.

Part ofMaths Numeracy (WJEC)Number

Mortgages

Buying a house is one of the biggest purchases a person can make. Most people have to get a special type of loan called a mortgage. The more money you borrow, the more you will pay back in interest payments. Also the longer you take to repay your mortgage the more interest you will pay.

The size of the mortgage you can have will depend on the size of your salary. A mortgage company tends to only lend 2½ times your salary.

If you are buying a property with someone else, the size of the mortgage will be based on both your salaries. The mortgage company normally uses the following calculation to work out how much to offer: 2½ times the largest salary plus 1 times the smaller salary. This is called the affordability calculator and tells the company whether you can afford to buy the house.

Affordability calculations

Single person affordability = 2.5 × (salary)

Two person affordability = 2.5 × (larger salary) + 1 × (smaller salary)

Example

A young couple want to move into a flat together. One earns £14,000 and the other earns £20,000. They have a deposit of £15,000. Can they afford a £130,000 flat which requires a 10% deposit?

Solution

No, the young couple can’t afford a £130,000 flat.

To work out the answer, it’s a good idea to break down the calculations into various steps:

1. Can they afford the deposit?

10 % of £130,000 = 0.10 × £130,000 = £13,000

Yes they can, as they have £15,000 which is more than the £13,000 required.

2. How much do they need to borrow?

£130,000 – £15,000 = £115,000

3. Can they afford the amount they would need to borrow?

Affordability = 2.5 × (larger salary) + 1 × (smaller salary)

= 2.5 × £20,000 + 1 × £14,000

= £64,000

4. Can they afford a £130,000 flat which requires a 10% deposit?

Although the young couple have enough for the deposit, they do not earn enough between them to be able to borrow £115,000 (only £65,000).

Question

Arron wants to buy his first house. He earns £44,000 and has a £50,000 deposit. He has found a house for £150,000 which he likes and he wants to get a mortgage with a 20% deposit. Is this possible?

Mortgage repayments

Leon is comparing mortgage figures for a property for which he needs a mortgage of £55,000. Using a mortgage calculator, he has worked out how his monthly payments would vary depending on the length of the mortgage he chooses.

A table showing how monthly payments vary depending on the length of the mortgage

Example

How much will he save by taking out a mortgage for 20 years instead of 30?

Solution

Each year has 12 months, so 20 years is calculated as 20 years × 12 months = 240 months.

Every month Leon pays £330.

£330 × 240 = £79,200

Each year has 12 months so 30 years has 30 × 12 = 360 months.

Every month Leon would pay £300 if he had taken the mortgage over 30 years.

£300 × 360 = £108,000.

Saving: £108,000 – £79,200 = £28,800

This means he has saved £28,800 by taking out a mortgage for 20 years, not 30.

Question

Using the same table, work out how much Leon would pay if he took out his mortgage for 25 years.