Question

A house worth £80,000 in January 2012 is set to decrease in value by 7% per year. What will the value of the house be in January 2015?

Answer 1

Given:

A house worth £80,000 in January 2012 is set to decrease in value by 7% per year.

To find:

What will the value of the house be in January 2015?

Solution:

To solve the above problem we will use the following formula of depreciation:

$\boxed{\bold{A = P [1 - \frac{R}{100} ]^n}}$

where

A = price after n years

P = current price

R = rate of decrease

n = no. of years

In 2012, the price of the house, P = £ 80,000

The rate of decrease in the value of the house per year, R = 7%

No. of years, n = 2015 - 2012 = 3 years

Now, on substituting the given values in the formula above, we get

$A = 80000 [1 - \frac{7}{100} ]^3$

$\implies A = 80000 [ \frac{100 - 7}{100} ]^3$

$\implies A = 80000 [ \frac{93}{100} ]^3$

$\implies A = 80000 [ 0.93 ]^3$

$\implies A = 80000 \times 0.8043$

$\implies \bold{ A = 64344}$

Thus, the value of the house in January 2015 will be → £ 64344.

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