Questions: An investor wants to save money to purchase real estate. He deposits 5575 at the end of each year in an ordinary annuity that pays 4% interest, compounded annually. (a) Find the total value of the annuity at the end of the 1st year. (b) Find the total value of the annuity at the end of the 2nd year. (c) Find the total value of the annuity at the end of the 3rd year.

(a) Find the total value of the annuity at the end of the \(1^{th}\) year.

Calculate the value after 1 year.

At the end of the first year, the investor deposits 5575. Since this is an ordinary annuity, the deposit is made at the end of the year. Thus, no interest is earned on the deposit during the first year. The value at the end of the first year is 5575.

\(\boxed{5575}\)

(b) Find the total value of the annuity at the end of the \(2^{nd}\) year.

Calculate the value after 2 years.

At the end of the second year, the investor deposits another 5575. The initial deposit has earned interest at a rate of 4% for one year. Value at the end of the second year: \(5575(1.04) + 5575 = 5575(1 + 1.04) = 5575(2.04) = 11373\)

\(\boxed{11373}\)

(c) Find the total value of the annuity at the end of the \(3^{rd}\) year.

Calculate the value after 3 years.

At the end of the third year, another 5575 is deposited. The previous two deposits have accumulated interest. Value at the end of the third year: \(5575(1.04)^2 + 5575(1.04) + 5575 = 5575(1.04^2 + 1.04 + 1) = 5575(1.0816 + 1.04 + 1) = 5575(3.1216) = 17422.62\)

\(\boxed{17422.62}\)

\(\boxed{5575}\) \(\boxed{11373}\) \(\boxed{17422.62}\)