Please show the work to solve this problem the correct answe

Please show the work to solve this problem the correct answer is A. I having trouble solving thank you.

Suppose that 1-year, 2-year, and 3-year forward prices for the Australian dollar are $1.05/A$, $0.98/A$, and $0.83/A$, respectively. The 1-year, 2-year, and 3-year effective annual interest rates in the U.S. are 5.8%, 6.6%, and 6.8%. What is the fixed exchange rate in a 3-year Australian dollar swap? (In other words, what 3-year U.S. dollar annuity is equivalent to a 3-year annuity of A$1?)

b. $0.85

c. $1.12

d. $1.03

e. $0.92

Solution

Let the fixed exchange rate be $ K per A $.

A three-year annuity of A$ 1 is same as a cash flow of $ 1.05 at the end of Year 1, $ 0.98 at the end of Year 2 and $ 0.83 at the end of Year 3. This is so because A$ 1 is equal to $ 1.05, $0.98 and $ 0.83 at the end of Year 1, Year 2 and Year 3 respectively.

Further, the total present value of these $ cash flows discounted at the effective annual interest rate prevailing at the end of each time period should be equal to the total present value of the three-year fixed dollar annuity discounted at the same prevailing interest rates.

Therefore, K x (1/1.058) + K x 1/(1.066)^(2) + K x 1/(1.068)^(3) = 1.05 / 1.058 + 0.98 / (1.066)^(2) + 0.83 / (1.068)^(3)

K x (1/1.058) + K x 1/(1.066)^(2) + K x 1/(1.068)^(3) = 2.5362

K = $ 0.9585 or $ 0.96 / A $ approximately.

Hence, the correct option is (A).