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Jamie invests £6000 at a simple interest rate of r% each year - OCR - GCSE Maths - Question 8 - 2021 - Paper 1

Question 8

Jamie invests £6000 at a simple interest rate of r% each year. After 6 years the value of their investment is £7170. Find the value of r.

Worked Solution & Example Answer:Jamie invests £6000 at a simple interest rate of r% each year - OCR - GCSE Maths - Question 8 - 2021 - Paper 1

Step 1

Find the Total Interest Earned

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Answer

To calculate the total interest earned over 6 years, we start by determining the total value of the investment after this period, which is given as £7170. The initial investment was £6000. Therefore, the total interest earned can be calculated as follows:

ext{Total Interest} = ext{Final Amount} - ext{Principal} = 7170 - 6000 = £1170

Step 2

Use the Simple Interest Formula

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Answer

The formula for simple interest is:

ext{Interest} = ext{Principal} imes ext{Rate} imes ext{Time}

In this case, we can substitute the known values into the formula to solve for r:

1170 = 6000 imes rac{r}{100} imes 6

Step 3

Solve for r

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Answer

Rearranging the equation to isolate r gives:

rac{r}{100} = rac{1170}{6000 imes 6}

Calculating the right side:

rac{1170}{36000} = rac{39}{1200} = 0.0325

Thus, we can now find r:

r = 0.0325 imes 100 = 3.25 ext{%}

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