Discuss and discover


Working with a classmate, complete the following task. You invest €1 000 in a start-up company and you get 20% increase on your investment at the end of the fi rst year. You get another 20% increase at the end of the second year, and so on. This means that at the end of each year, the value of the investment is worth 120% of the value it was at the start of the year.


Copy and complete the table provided to show the value of your investment over six years.


(time elapsed) Increase by % Pattern 0 (start) 1 2 3


Year, t


20 20 ….


4 5 6


… t


(i) How much money was the fi rst 20% increase equal to?


(ii) How much money was the second 20% increase equal to?


(iii) Explain, in your own words, why the second 20% increase is greater than the fi rst 20% increase.


(iv) Copy the graph provided and plot the time that has passed against the value of the investment.


(v) This graph represents one of the following patterns: (i) linear (ii) quadratic (iii) exponential. Which type of pattern does it represent? Justify your answer.


(vi) Describe in your own words what is happening to the value of the investment, as the time increases.


(vii) Using a mathematical strategy, calculate the value of the investment at the end of 15 years. Explain in words how you got this answer.


Taking it FURTHER


(viii) Explain in words how you could fi nd the value of any investment amount after any number of years, at any interest rate.


y


2 400 2 600


1 000 1 400 1 800 2 200


1 200 1 600 2 000


800 600 400 200


0 1 2 3 4 Time (years) 5 6 x 1 000 × 1.2 1 000 × 1.2 × 1.2


Rule for pattern Value (€) 1 000


1 000(1·2)1 1 000(1·2)2


1 200 1 440


Section B Advancing mathematical ideas


271


17 Managing your money


Amount (€)


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