At the beginning of 2009, Mr Veale bought a company. The value of the company was £50,000 Each year the value of the company increased by 2%. (a) Calculate the value of the company at the beginning of 2017 Give your answer correct to the nearest £100 At the beginning of 2009 the value of a different company was £250,000 In 6 years the value of this company increased to £325,000 This is equivalent to an increase of x% each year. (b) Find the value of x. Give your answer correct to 2 significant figures.

GCSE Edexcel Maths Simple & Compound Interest, Growth & Decay: At the beginning of 2009, Mr Vea

At the beginning of 2009, Mr Veale bought a company - Edexcel - GCSE Maths - Question 13 - 2017 - Paper 2

Question 13

At the beginning of 2009, Mr Veale bought a company. The value of the company was £50,000 Each year the value of the company increased by 2%. (a) Calculate the val... show full transcript

Worked Solution & Example Answer:At the beginning of 2009, Mr Veale bought a company - Edexcel - GCSE Maths - Question 13 - 2017 - Paper 2

Step 1

Calculate the value of the company at the beginning of 2017

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Answer

To find the value of the company at the beginning of 2017, we need to account for the 2% annual increases over 8 years (from 2009 to 2017).

The formula to calculate the future value considering compound interest is:

$FV = PV imes (1 + r)^n$

where:

$FV$ is the future value.
$PV$ is the present value (£50,000).
$r$ is the rate of increase (0.02 for 2%).
$n$ is the number of years (8).

Plugging in the values:

$FV = 50000 imes (1 + 0.02)^8$ $FV = 50000 imes (1.02)^8 \approx 50000 \times 1.171659 \approx 58583.23$

Rounding to the nearest £100, the value of the company at the beginning of 2017 is approximately £58,600.

Step 2

Find the value of x

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Answer

We can use the formula for compound growth to determine the annual percentage increase $x$ :

For the company starting at £250,000 and increasing to £325,000 over 6 years, we set:

$325000 = 250000 imes (1 + \frac{x}{100})^6$

Dividing both sides by £250,000 gives:

$\frac{325000}{250000} = (1 + \frac{x}{100})^6$ $1.3 = (1 + \frac{x}{100})^6$

To solve for $1 + \frac{x}{100}$ , we take the sixth root:

$1 + \frac{x}{100} = 1.3^{\frac{1}{6}} \approx 1.045$

Now, subtracting 1: $\frac{x}{100} \approx 0.045$

Thus, $x \approx 4.5$ . Therefore, the value of x is approximately 4.5%.

At the beginning of 2009, Mr Veale bought a company - Edexcel - GCSE Maths - Question 13 - 2017 - Paper 2

Worked Solution & Example Answer:At the beginning of 2009, Mr Veale bought a company - Edexcel - GCSE Maths - Question 13 - 2017 - Paper 2

Calculate the value of the company at the beginning of 2017

Find the value of x

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