Final answer:
To calculate the interest earned with simple interest, use the formula I = P * R * T. To calculate the interest earned with compound interest, use the formula A = P * (1 + R/n)^(n*T) - P. The difference in interest earned between compound interest and simple interest is $767.34.
Step-by-step explanation:
To calculate the interest earned with simple interest, we use the formula: I = P * R * T, where P is the principal amount, R is the interest rate, and T is the time in years. In this case, our principal is $4000, the interest rate is 6%, and the time is 5 years. Therefore, the interest earned with simple interest is: I = 4000 * 0.06 * 5 = $1200.
To calculate the interest earned with compound interest, we use the formula: A = P * (1 + R/n)^(n*T), where A is the final amount, P is the principal amount, R is the interest rate, n is the number of times interest is compounded per year, and T is the time in years. In this case, our principal is $4000, the interest rate is 6%, and the time is 5 years. Since the interest is compounded daily, n would be 365. Therefore, the interest earned with compound interest is: A = 4000 * (1 + 0.06/365)^(365*5) - 4000 = $1967.34.
The difference in interest earned between compound interest and simple interest is: $1967.34 - $1200 = $767.34. Therefore, the correct answer is A. $767.34.