Final answer:
To accumulate $9,000 in 8 years with an account that earns 5% compounded semiannually, a student should deposit $5,700.
Step-by-step explanation:
To determine the amount of money that should be deposited today in an account that earns 5% compounded semiannually to accumulate $9,000 in 8 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the future value
- P is the principal amount (the amount to be deposited)
- r is the annual interest rate expressed as a decimal
- n is the number of compounding periods per year
- t is the number of years
Plugging in the given values, we have:
9000 = P(1 + 0.05/2)^(2*8)
Solving for P, we find that the amount of money that should be deposited is $5,700. Therefore, the correct answer is option B: $5,700.