# Gary brought a house for £235000. In the first year the value of the house depreciated by 5%. In each of the years 2,3, and 4 the value of the house increased by 7%. Work out the value of the house at the end of the fourth year?

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### Yassin Ahmed

I’ll make maths your favourite subject.

This question is testing your understanding of multipliers. In the first year Since the house value depreciated by 5% the multiplier we use is: 100% - 5% = 95% = 0.95 So we multiply £235,000 by 0.95 which gives us: £223,250. Let’s move on to the second year: Since the house value increases now, our multiplier is: 100% + 7% = 107% = 1.07 so we multiply the current house value which is £223,250 by 1.07 which gives: £238,877.50 in the third year as the house value increases by the same percentage we again use a multiplier of 1.07. £238,877.50 x 1.07 = £255,598.925 (note I dId not round mt value here as I have not finished the question yet) in the fourth year we do the same thing again as the house value increases by 7%. £255,598.925x 1.07 = £273,490.85 Thus by the end of the fourth year the house value is: £273,490.85 _____________________________________________ Alternatively if you are more advanced and comfortable with multipliers you can instantly do the following sum: £235,000 x 0.95 x (1.07)^3 = £273,490.85 Where the ^3 means cubed. This is because for three years the house value increased by 7%. Hope this makes sense, if not give me a message.

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