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. \( 5 \square \)

We are given that the investor makes deposits of $550 at the end of each year (ordinary annuity). The annual interest rate is 8% compounded annually. For an ordinary annuity, the deposit made at the end of the year does not earn interest until the next period. Thus, the value at the end of year n is the sum of each deposit accumulated with interest for the number of years it has been invested. (a) End of the 1st year: • Only one payment of $550 is made at the end of the 1st year and no interest is accrued on that deposit at that time.   Total value = $550 (b) End of the 2nd year: • The deposit at the end of Year 1 grows for one year: 550 × 1.08 • Plus the deposit made at the end of Year 2, which does not earn any interest yet.   Total value = 550 × 1.08 + 550 Calculate:   550 × 1.08 = 594   Total value = 594 + 550 = 1144 (c) End of the 3rd year: • The deposit at the end of Year 1 grows for two years: 550 × (1.08)² • The deposit at the end of Year 2 grows for one year: 550 × 1.08 • The deposit at the end of Year 3 does not earn interest.   Total value = 550 × (1.08)² + 550 × 1.08 + 550 Calculate each term:   (1.08)² = 1.1664  so  550 × 1.1664 = 641.52 (exact)   550 × 1.08 = 594   Adding the deposit: 550 Now sum them:   Total value = 641.52 + 594 + 550 = 1785.52 Thus, the answers are: (a) $550 (b) $1144 (c) $1785.52