Question

At the start of 2014 Tim's house was worth £100 000.

The value of the house increased by 10% every year.
Work out the value of his house at the start of 2018.

Answer 1

$146,410

Explanation:

You want to know the value of a house at the start of 2018 that is worth £100 000 at the start of 2014, and increases in value 10% per year.

Increased value

The value at the start of 2015 is ...

£100 000 × (1 +10%) = £110 000

The next year, the value is ...

£110 000 × 1.10 = £121 000

After 2 more years, the value at the start of 2018 is ...

£121 000 × 1.10² = £146 410

At the start of 2018, the value of Tim's house is £146 410.

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Additional comment

Essentially, the value compounds. The increased value after 1 year is the basis of the value increase for the next year. This makes the value an exponential function, rather than the linear function it would be if the value increased by £10 000 per year.

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Answer 2

£146,410

Explanation:

We know

From 2014 to 2018 is 4 years

1 year = 10% increase

1 + 10% = 1.10

We take

100,000 x
`1.10^(4)` = £146,410

So, the house is £146,410 at the start of 2018.