Question 1: Calculate the amount after 30 days if £1000 is invested at an annual interest rate of 6%, compounded daily. Use the formula: A = P(1 + r/n)^(nt).

Answer: 1018.21

Question 2: What is the daily interest rate (r/n) if a £500 investment grows to £510 after 10 days, assuming daily compounding?

Answer: 0.002

Question 3: A bank offers an interest rate of 4% per annum, compounded daily. How much will a £2000 deposit grow to after 60 days?

Answer: 2024.22

Question 4: If an investment of £1500 earns interest daily at an annual rate of 5%, what is the interest earned after 45 days?

Answer: £9.52

Question 5: Construct the compound interest formula for daily compounding and explain each part briefly.

Answer: A = P(1 + r/n)^(nt); where P is principal, r is annual rate, n is number of days in a year, t is time in years, A is the amount after t years.

Question 6: Calculate how many days it takes for £1000 to double if invested at 7% annual interest compounded daily.

Answer: 104 days

Question 7: A savings account offers 3.5% interest annually, compounded daily. How much interest is earned on £2500 after 90 days?

Answer: £22.79

Question 8: What are common mistakes students make when calculating daily compound interest? Identify and correct a typical error.

Answer: Using annual rate directly without dividing by 365, leading to overestimation. Correct by dividing the rate by 365 for daily interest.

Question 9: A £1200 investment grows to £1250 after 15 days at daily compounding interest. Find the daily interest rate.

Answer: 0.0026

Question 10: Challenge: If you invest £5000 at 8% annual interest compounded daily, how long will it take to reach £5500?

Answer: Approximately 135 days