Final answer:
To find the interest rate if £5000 grows to £5984 in 2 years, calculate the interest earned (£984), then divide by the product of the principal and time (£10000). This results in a total interest rate of 9.84% over 2 years, or 4.92% per year when rounded to one decimal place.
Step-by-step explanation:
Calculating the Interest Rate
To find the interest rate given that £5000 has a future value of £5984 in 2 years, we will use the formula for simple interest which is:
Interest = Principal × rate × time
First, let's calculate the total interest earned:
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- Interest earned = Future Value - Principal
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- Interest earned = £5984 - £5000
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- Interest earned = £984
Now, let's rearrange the formula to solve for the rate:
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- rate = Interest / (Principal × time)
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- rate = £984 / (£5000 × 2)
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- rate = £984 / £10000
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- rate = 0.0984 or 9.84%
This rate is the total interest over 2 years. To find the annual rate, we divide by the number of years:
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- Annual interest rate = Total rate / Number of years
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- Annual interest rate = 9.84% / 2
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- Annual interest rate = 4.92%
After rounding to one decimal place, the annual interest rate is 4.9%, which is not listed in the options given. Therefore, it appears there may either be an error in the options or in the interpretation of the question as none of the provided options match the calculated rate. The closest option is C) 4.8%.