Question 1: Calculate the amount of money accumulated after 30 days if $1,000 is invested at an annual interest rate of 12%, compounded daily. Use the formula: A = P(1 + r/n)^{nt}.

Answer: A = 1000 * (1 + 0.12/365)^{365*30/365}

Question 2: What is the effective daily interest rate if the annual rate is 12% compounded daily?

Answer: 0.0329%

Question 3: Calculate the interest earned in 15 days on a $2,500 investment with daily compounding at 10% annual rate.

Answer: Interest = 2500 * [(1 + 0.10/365)^{15} - 1]

Question 4: Construct a scenario where daily compounding results in more interest earned than monthly compounding over the same period. Briefly explain your reasoning.

Answer: Students should recognize that daily compounding applies interest more frequently, leading to higher overall interest than monthly over the same time.

Question 1: A bank offers 12% interest compounded daily. How much will a $1,200 investment grow to after 45 days? Show all calculations.

Answer: A = 1200 * (1 + 0.12/365)^{45}

Question 2: If a person invests $500 at 9% annual interest compounded daily, what is the total amount after 60 days? Explain your steps.

Answer: A = 500 * (1 + 0.09/365)^{60}

Question 3: A student claims that daily compounding always produces more interest than weekly or monthly compounding, regardless of the interest rate. Is this statement true? Justify your answer.

Answer: Students should recognize that higher frequency of compounding generally yields more interest, but the difference depends on the rate and period.

Question 4: Calculate the total interest earned on a $1,500 investment over 20 days at 8% annual interest compounded daily. Show your working.

Answer: Interest = 1500 * [(1 + 0.08/365)^{20} - 1]

Question 1: An online savings account offers 10% interest compounded daily. If you deposit $5,000, how much will you have after 90 days? Illustrate your calculation process.

Answer: A = 5000 * (1 + 0.10/365)^{90}

Question 2: A business invests $10,000 at an annual interest rate of 15% compounded daily. How much interest will accrue after 120 days? Explain your steps.

Answer: Interest = 10000 * [(1 + 0.15/365)^{120} - 1]

Question 1: Compare the total amounts after 60 days for a $2,000 investment at 10% interest compounded daily vs. monthly. Which yields more and why? Support your reasoning with calculations.

Answer: Compare A_daily = 2000 * (1 + 0.10/365)^{60} and A_monthly = 2000 * (1 + 0.10/12)^{2} (for 2 months).

Question 2: If the interest rate increased to 20% annually, how would this affect the amount after 30 days on a $3,000 investment? Calculate and compare with the original rate.

Answer: Original: 3000 * (1 + 0.10/365)^{30}; New: 3000 * (1 + 0.20/365)^{30}

Question 1: A student calculates interest over 60 days using A = P(1 + r)^t, where r is the annual rate and t is days. Is this correct? If not, fix the formula.

Answer: Incorrect; should be A = P(1 + r/n)^{nt} with n=365.

Question 2: A teacher states that for daily compounding, the interest for 1 day is simply annual rate divided by 365. Is this correct? Explain.

Answer: Correct; daily interest rate = annual rate / 365.

Question 3: Calculate interest on $4,000 at 12% annual rate for 45 days using simple interest formula (Interest = Principal x Rate x Time). Is this appropriate for daily compounding? Why or why not?

Answer: No; simple interest doesn't account for compounding. Use compound formula for accuracy.