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How much money should be deposited today in an account that earns 5% compounded semiannually so that it will accumulate $9,000 in 8 years?

A. $5,500
B. $5,700
C. $6,000
D. $6,500

1 Answer

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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.

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