An investor wants to save money to purchase real estate. He deposits \( \$ 550 \) at the end of each year in an ordinary annuity that pays \( 8 \% \) interest, compounded annually. Answer each part. Do not round any Intermediate computations nor answers. If necessary, refer to the list of financial formulas. (a) Find the total value of the annuity at the end of the \( 1^{\text {st }} \) year. (b) Find the total value of the annuity at the end of the \( 2^{\text {nd }} \) year, (c) Find the total value of the annuity at the end of the \( 3^{\text {nd }} \) year. \( 5 \square \)

To solve the problem, we will calculate the total value of the ordinary annuity at the end of each specified year using the formula for the future value of an ordinary annuity. The future value of an ordinary annuity can be calculated using the formula: \[ FV = P \times \frac{(1 + r)^n - 1}{r} \] where: - \( FV \) = future value of the annuity - \( P \) = annual payment - \( r \) = interest rate - \( n \) = number of years Given: - \( P = 550 \) - \( r = 0.08 \) (a) **Total value at the end of the 1st year:** \[ FV_1 = 550 \times \frac{(1 + 0.08)^1 - 1}{0.08} = 550 \times \frac{1.08 - 1}{0.08} = 550 \times \frac{0.08}{0.08} = 550 \times 1 = 550 \] So, the total value at the end of the 1st year is **\$550**. (b) **Total value at the end of the 2nd year:** \[ FV_2 = 550 \times \frac{(1 + 0.08)^2 - 1}{0.08} = 550 \times \frac{1.1664 - 1}{0.08} = 550 \times \frac{0.1664}{0.08} = 550 \times 2.08 = 1144 \] So, the total value at the end of the 2nd year is **\$1,144**. (c) **Total value at the end of the 3rd year:** \[ FV_3 = 550 \times \frac{(1 + 0.08)^3 - 1}{0.08} = 550 \times \frac{1.259712 - 1}{0.08} = 550 \times \frac{0.259712}{0.08} = 550 \times 3.2464 = 1786.52 \] So, the total value at the end of the 3rd year is **\$1,786.52**.