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Jean invests £1200 in an account paying compound interest for 2 years - Edexcel - GCSE Maths - Question 10 - 2018 - Paper 2
Question 10
Jean invests £1200 in an account paying compound interest for 2 years. In the first year the rate of interest is x%. At the end of the first year the value of Jean's... show full transcript
Worked Solution & Example Answer:Jean invests £1200 in an account paying compound interest for 2 years - Edexcel - GCSE Maths - Question 10 - 2018 - Paper 2
Step 1
In the first year the rate of interest is x%.
Answer
To find the rate of interest, we start with the formula for compound interest:
[ A = P(1 + r)^t ]
Where:
- A is the amount after t years (£12336)
- P is the principal (£1200)
- r is the rate of interest in decimal form
- t is the time period in years (1)
Setting this up, we have:
[ 12336 = 1200(1 + \frac{x}{100}) ]
To isolate (1 + \frac{x}{100}), divide both sides by 1200:
[ 1 + \frac{x}{100} = \frac{12336}{1200} \approx 10.28 ]
Subtract 1:
[ \frac{x}{100} = 9.28 ]
Multiply by 100:
[ x \approx 928 % ]
Step 2
In the second year the rate of interest is \( \frac{x}{2} \%.
Answer
Now, substituting (x = 928)% into (\frac{x}{2}), we get:
[ \frac{928}{2} = 464 % ]
For the second year, we again use the compound interest formula. The principal is now the amount from the first year (£12336):
[ A = 12336(1 + \frac{464}{100}) ]
Calculating:
[ A = 12336(1 + 4.64) = 12336 \times 5.64 \approx 69653.44 ]
Thus, at the end of 2 years, Jean's investment is approximately £69653.44.