Question 1: If $1000 is invested at an annual interest rate of 12%, compounded daily, what is the value after 1 day? Use the formula A = P (1 + r/n)^(nt).

Answer: 1000 * (1 + 0.12/365)^(1) ≈ 1000.33

Question 2: Calculate the amount after 3 days if $500 is invested at an annual rate of 6%, compounded daily.

Answer: 500 * (1 + 0.06/365)^(3) ≈ 500.25

Question 3: A principal of $2000 earns 8% interest per year compounded daily. What is the interest earned after 1 day?

Answer: 2000 * (1 + 0.08/365)^(1) - 2000 ≈ 0.44

Question 4: Simplify the expression for the amount after 2 days: A = 1500 * (1 + 0.10/365)^(2).

Answer: 1500 * (1 + 0.10/365)^2

Question 5: A principal of $800 is invested at 9% annual interest, compounded daily. What is the total amount after 7 days?

Answer: 800 * (1 + 0.09/365)^7 ≈ 801.66

Question 6: A loan of $1500 has an interest rate of 10% per year compounded daily. How much interest is accrued after 5 days?

Answer: (1500 * (1 + 0.10/365)^5) - 1500 ≈ 2.05

Question 7: If a sum of money doubles in 60 days with daily compounding, what is the approximate daily interest rate?

Answer: (2) = (1 + r)^60; r ≈ (2)^{1/60} - 1 ≈ 0.01155 or 1.155%

Question 8: A savings account with $1200 earns 5% interest compounded daily. How much money will be in the account after 30 days?

Answer: 1200 * (1 + 0.05/365)^30 ≈ 1204.90

Question 9: A principal of $1000 is invested at 12% annual interest compounded daily for 10 days. How much interest is earned?

Answer: (1000 * (1 + 0.12/365)^10) - 1000 ≈ 0.33

Question 10: An account balance grows from $5000 to $5060 in 14 days with daily compounding. What is the approximate daily interest rate?

Answer: (1 + r)^14 = 5060/5000 ≈ 1.012; r ≈ (1.012)^{1/14} - 1 ≈ 0.00085 or 0.085%