Question

Rami bought a house on 1st January 2015. In2015 the house increased in value by 15%. In 2016 the house decreased in value by 8%. On 1st January 2017 the value of the house was $687700. What was the value of the house on 1st January 2015

Answer 1

Answer:

The value of the house on 1st January 2015 was of $650,000.

Step-by-step explanation:

Decimal multipliers:

For a increase of a%, the decimal multiplier is given by $\frac{100+a}{100}$

For a decrease of a%, the decimal multiplier is given by $\frac{100-a}{100}$

Rami bought a house on 1st January 2015.

For a value of x.

In 2015 the house increased in value by 15%.

This means that x is multiplied by $\frac{100+15}{100} = \frac{115}{100} = 1.15$

In 2016 the house decreased in value by 8%.

This means that 1.15 times x is multiplied by $\frac{100-8}{100} = \frac{92}{100} = 0.92$

On 1st January 2017 the value of the house was $687700.

The value of these multiplications is 687700.

What was the value of the house on 1st January 2015?

This is x, so:

$x*1.15*0.92 = 687700$

$x = \frac{687700}{1.15*0.92}$

$x = 650000$

The value of the house on 1st January 2015 was of $650,000.