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Naoby invests £6000 for 5 years - Edexcel - GCSE Maths - Question 10 - 2017 - Paper 3

Question 10

Naoby invests £6000 for 5 years. The investment gets compound interest of x% per annum. At the end of 5 years the investment is worth £8029.35 Work out the value of ... show full transcript

Worked Solution & Example Answer:Naoby invests £6000 for 5 years - Edexcel - GCSE Maths - Question 10 - 2017 - Paper 3

Step 1

Calculate the final amount formula

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Answer

The formula for compound interest is given by:

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

where:

A is the amount of money accumulated after n years, including interest.
P is the principal amount (£6000).
r is the annual interest rate (expressed as a decimal).
t is the time the money is invested for in years (5 years in this case).

Step 2

Set up the equation

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Answer

Using the final amount (£8029.35), we can rewrite the equation as:

$8029.35 = 6000(1 + \frac{x}{100})^5$

Step 3

Solve for x

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Answer

First, isolate the term containing x:

$\frac{8029.35}{6000} = (1 + \frac{x}{100})^5$

Calculating the left side:

$\frac{8029.35}{6000} \approx 1.338225$

Now take the 5th root:

$1 + \frac{x}{100} = 1.338225^{\frac{1}{5}}$

Calculating the right side yields approximately 1.0625:

$1 + \frac{x}{100} \approx 1.0625$

Subtract 1 from both sides:

$\frac{x}{100} \approx 0.0625$

Thus, multiply by 100:

$x \approx 6.25$

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