The value of a house, £H, is given by the formula H = 165000 × 1.03^i where i is the number of years after 1st January 2010. (a) Write down the value of the house on 1st January 2010. (b) Write down the annual percentage increase in the value of the house. (c) Show that the value of the house is over £200000 on 1st January 2017.

GCSE OCR Maths Indices: The value of a house, £H, is giv

The value of a house, £H, is given by the formula H = 165000 × 1.03^i where i is the number of years after 1st January 2010 - OCR - GCSE Maths - Question 10 - 2019 - Paper 4

Question 10

The value of a house, £H, is given by the formula H = 165000 × 1.03^i where i is the number of years after 1st January 2010. (a) Write down the value of the house... show full transcript

Worked Solution & Example Answer:The value of a house, £H, is given by the formula H = 165000 × 1.03^i where i is the number of years after 1st January 2010 - OCR - GCSE Maths - Question 10 - 2019 - Paper 4

Step 1

(a) Write down the value of the house on 1st January 2010.

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Answer

To find the value of the house on 1st January 2010, we substitute i = 0 into the formula:

$H = 165000 × 1.03^0 = 165000 × 1 = 165000$

Thus, the value of the house on 1st January 2010 is £165,000.

Step 2

(b) Write down the annual percentage increase in the value of the house.

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Answer

The annual percentage increase in the value of the house is given by the growth factor. Since the formula for the house value includes the term 1.03, the annual percentage increase is:

$ext{Percentage Increase} = (1.03 - 1) × 100\% = 3\%$

Therefore, the annual percentage increase in the value of the house is 3%.

Step 3

(c) Show that the value of the house is over £200000 on 1st January 2017.

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Answer

To determine the value of the house on 1st January 2017, we calculate the value by substituting i = 7 (since 2017 is 7 years after 2010) into the formula:

$H = 165000 × 1.03^7$

Calculating this, we find:

$H = 165000 × 1.225043 = 202,920.18$

This value, £202,920.18, is indeed greater than £200,000, confirming that the value of the house is over £200,000 on 1st January 2017.

The value of a house, £H, is given by the formula H = 165000 × 1.03^i where i is the number of years after 1st January 2010 - OCR - GCSE Maths - Question 10 - 2019 - Paper 4

Worked Solution & Example Answer:The value of a house, £H, is given by the formula H = 165000 × 1.03^i where i is the number of years after 1st January 2010 - OCR - GCSE Maths - Question 10 - 2019 - Paper 4

(a) Write down the value of the house on 1st January 2010.

(b) Write down the annual percentage increase in the value of the house.

(c) Show that the value of the house is over £200000 on 1st January 2017.

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