Question 1: Calculate the amount after 1 day if $1,000 is invested at an annual interest rate of 5%, compounded daily. Use the formula A = P(1 + r/n)^(nt).

Answer: A ≈ 1000 * (1 + 0.05/365)^(365*1/365) ≈ 1000 * 1.00013699 ≈ 1001.37

Question 2: If you invest $500 at an annual interest rate of 6% compounded daily, what will be the amount after 3 days?

Answer: A ≈ 500 * (1 + 0.06/365)^(365*3/365) ≈ 500 * 1.00049315 ≈ 500.25

Question 3: A savings account offers 4% annual interest compounded daily. How much interest is earned in 1 day on a $2,000 deposit?

Answer: Interest ≈ 2000 * (1 + 0.04/365) - 2000 ≈ 2000 * 0.00010959 ≈ $0.219

Question 4: Construct a graph showing the growth of a $1,000 investment over 7 days at 3% annual interest compounded daily. Label the axes.

Answer: Students plot points for A = 1000*(1 + 0.03/365)^(d), d=1..7

Question 5: A bank offers a special daily compounded interest rate that results in a 0.1% increase per day. What is the equivalent annual interest rate?

Answer: Effective annual rate ≈ (1 + 0.001)^365 - 1 ≈ 1.4407 - 1 ≈ 44.07%

Question 6: How much will a $1,200 investment grow to after 10 days at 8% annual interest compounded daily?

Answer: A ≈ 1200 * (1 + 0.08/365)^(365*10/365) ≈ 1200 * 1.00219 ≈ 1226.60

Question 7: A person invests $750 at an annual interest rate of 5.5%, compounded daily. How many days will it take for the investment to double?

Answer: Solve 2*750 = 750*(1+0.055/365)^d → 2 = (1.00015068)^d → d ≈ ln(2)/ln(1.00015068) ≈ 4629 days (~12.67 years)

Question 8: In a real-world scenario, if an account grows from $2,000 to $2,100 over 4 days with daily compounding, what is the approximate daily interest rate?

Answer: 1 + r = (2100/2000)^(1/4) ≈ 1.0123 → r ≈ 1.23%

Question 9: Identify and correct the mistake: A student used the formula A = P(1 + r)^t for daily compounding, assuming r is annual interest rate. Why is this incorrect?

Answer: The mistake is not dividing the annual rate by 365. For daily compounding, r should be the daily rate (annual rate divided by 365).

Question 10: A $3,000 investment at 7% annual interest compounded daily is left for 6 days. What is the interest earned?

Answer: Interest ≈ 3000 * (1 + 0.07/365)^6 - 3000 ≈ 3000 * 1.00115 - 3000 ≈ $3.45