Rashid invests money into an account which pays a fixed rate of compound interest each year - OCR - GCSE Maths - Question 4 - 2017 - Paper 1
Question 4
Rashid invests money into an account which pays a fixed rate of compound interest each year. The value, V, of his investment after t years is given by the formula
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Worked Solution & Example Answer:Rashid invests money into an account which pays a fixed rate of compound interest each year - OCR - GCSE Maths - Question 4 - 2017 - Paper 1
Step 1
How much money did Rashid invest?
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Answer
To determine how much Rashid invested, we can observe the formula presented:
V=1250×1.03t.
Here, the initial investment, often referred to as the principal amount, is the coefficient of the exponential term. Therefore, Rashid invested £1250.
Step 2
What rate of compound interest is paid each year?
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Answer
The formula indicates an annual growth factor of 1.03. To find the annual rate of compound interest, subtract 1 from the growth factor and express it as a percentage:
Rate=(1.03−1)×100%=0.03×100%=3%.
Thus, the rate of compound interest paid each year is 3%.
Step 3
Circle the graph that best represents the growth in Rashid's account.
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Answer
The graph that best represents the growth of Rashid's investment should be an exponential curve, indicating that as time increases, the value of the investment grows more rapidly. Therefore, the third graph should be indicated as correct.
