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 apply the formula for compound interest:

$V = P(1 + r)^t$

where:

$V$ is the future value of the investment/loan, including interest.
$P$ is the principal investment amount (the initial deposit or loan amount).
$r$ is the annual interest rate (decimal).
$t$ is the number of years the money is invested or borrowed for.

Given:

$P = 50000$
$r = 0.02$
$t = 2017 - 2009 = 8$ (years)

Substituting these values into the formula:

$V = 50000(1 + 0.02)^8$

Calculating this gives:

$V = 50000(1.02)^8$

$$ V \\ ≈ 58583.00 $$ Rounding this to the nearest £100 gives: **£58,600**

Step 2

Find the value of x.

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Answer

To find the annual percentage increase x for the second company, we can use the formula for compound interest, similar to part (a). Here we know:

Initial value $P = 250,000$
Final value $V = 325,000$
Time $t = 6$ years.

We rearrange the formula to solve for the growth rate:

$V = P(1 + r)^t$ $325000 = 250000(1 + r)^6$

Dividing both sides by 250,000:

$(1 + r)^6 = rac{325000}{250000}$ $(1 + r)^6 = 1.3$

Now, taking the sixth root:

$1 + r = (1.3)^{1/6}$ $r \\ ≈ 1.0452 - 1$ $r \\ ≈ 0.0452$

Multiplying by 100 to convert it to a percentage:

$x \\ ≈ 4.52 \%$

Rounding this to 2 significant figures gives: 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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