Question 1: Calculate the amount after 3 years if £1000 is invested at an annual growth rate of 5%.

Answer: 1157.63

Question 2: What is the growth factor per year if an investment grows by 8% annually?

Answer: 1.08

Question 3: A sum of £500 is invested with an annual growth rate of 4%. Find the value of the investment after 2 years.

Answer: 540.80

Question 4: Construct a diagram showing the growth of £200 over 4 years at an annual growth rate of 3%.

Answer: Student draws exponential growth curve fitting the data points.

Question 5: A investment grows from £1500 to £1800 in 3 years. Find the annual growth rate, correct to 2 decimal places.

Answer: 3.20

Question 6: A company’s savings account increases by 6% each year. If the current balance is £2000, what will be the balance after 5 years?

Answer: 2674.56

Question 7: Explain why using the growth factor (e.g., 1 + r) is important when applying the growth formula.

Answer: It allows for straightforward multiplication of the initial amount by the compounded growth factor each year, accurately modeling percentage increase.

Question 8: A principal of £1200 grows to £1440 in 4 years. Show step-by-step how to find the annual growth rate, and state the rate as a percentage.

Answer: Growth factor = 1440/1200 = 1.2. (1 + r)^4 = 1.2. r = (1.2)^(1/4) - 1 ≈ 0.046, or 4.6%.

Question 9: A savings account increases by 7% annually. How many years will it take for an initial £500 to grow to at least £700?

Answer: Approximately 6 years.

Question 10: An investment of £800 grows to £1200 in 5 years. Is the annual growth rate consistent with the growth formula? Show your working.

Answer: Growth factor = 1200/800 =1.5. (1 + r)^5 = 1.5. r = (1.5)^(1/5) - 1 ≈ 0.084, or 8.4%. Yes, consistent with 8% annual growth.

Question 11: Identify and correct the common mistake: A student calculates the growth rate as (Final - Initial) / Years. Why is this incorrect?

Answer: This method does not account for compound growth, leading to incorrect annual growth rate. The correct method involves using the growth factor and roots.