(a) For annual compounding, we can use the formula for compound interest:
A = P * (1 + r/n)^(n*t),
where A is the future value of the investment, P is the initial principal, r is the interest rate, n is the number of compounding periods per year, and t is the number of years.
In this case, P = $5500, r = 8% = 0.08, n = 1 (since it's annual compounding), and t = 5.
Using these values, the formula becomes:
A = 5500 * (1 + 0.08/1)^(1*5) = $7954.29 (rounded to the nearest cent).
Therefore, the value of the investment at the end of 5 years for annual compounding is $7954.29.
(b) For semiannual compounding, we need to use the same formula, but with n = 2 (since there are two compounding periods per year).
Using the values P = $5500, r = 8% = 0.08, n = 2, and t = 5, the formula becomes:
A = 5500 * (1 + 0.08/2)^(2*5) = $7993.71 (rounded to the nearest cent).
Therefore, the value of the investment at the end of 5 years for semiannual compounding is $7993.71.
(c) For monthly compounding, we again use the same formula, but with n = 12 (since there are 12 compounding periods per year).
Using the values P = $5500, r = 8% = 0.08, n = 12, and t = 5, the formula becomes:
A = 5500 * (1 + 0.08/12)^(12*5) = $8003.73 (rounded to the nearest cent).
Therefore, the value of the investment at the end of 5 years for monthly compounding is $8003.73.
(d) For daily compounding, we once again use the same formula, but with n = 365 (assuming a non-leap year).
Using the values P = $5500, r = 8% = 0.08, n = 365, and t = 5, the formula becomes:
A = 5500 * (1 + 0.08/365)^(365*5) = $8006.30 (rounded to the nearest cent).
Therefore, the value of the investment at the end of 5 years for daily compounding is $8006.30.