Answer:
US$ 7,112.83 should be deposited today in an account that earns 8 % compounded semi-annually so that it will accumulate US$ 9,000 in 3 years.
Explanation:
1. Let's review the data given to us for solving the question:
Future Value = US$ 9,000
Annual interest rate = 8% compounded semi-annually = 4% each semester
Duration of the investment = 3 years = 6 semesters
2. Let's find the initial investment, using the following formula:
FV = PV * (1 + r) ⁿ
Replacing with the real values, we have:
9,000 = PV * (1 + 0.04) ⁶
9,000 = PV * (1.04) ⁶
9,000 = PV * 1.26531902
PV = 9,000/1.26531902
PV = US$ 7,112.83