Final answer:
To calculate the interest earned, use the formula A = P(1 + r/n)^(nt) - P. Plugging in the values, the interest earned is approximately $14.56 in 30 days.
Step-by-step explanation:
To calculate the interest earned in this scenario, we can use the formula: A = P(1 + r/n)^(nt) - P, where A is the total amount including principal and interest, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years. In this case, the principal amount is $4,500, the annual interest rate is 5.5%, the interest is compounded daily, and the time is 30 days. Plugging these values into the formula, we get A = 4500(1 + 0.055/365)^(365*30) - 4500. Calculating this expression gives us the total amount including interest. To find the interest earned, we subtract the principal amount from the total amount.
Let's calculate it step by step:
Convert the annual interest rate to a decimal: 5.5% = 0.055
Divide the annual interest rate by the number of compounding periods in a year: 0.055 / 365 = 0.00015
Calculate the number of compounding periods: 365 * 30 = 10,950
Calculate the total amount including interest: A = 4500(1 + 0.00015)^(10,950) - 4500
Calculate the interest earned: Interest = A - P
Plugging in the values, we get A ≈ $4,514.56 and Interest ≈ $14.56. So, you will earn approximately $14.56 in interest in 30 days.