How much money should be deposited in an account that earns 8% compounded semi-annually so that it will accumulate $9,000 in three years

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.

Step-by-step 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 amount that should be deposited today, 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

Note: Same answer to question 14017214, answered by me.