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Company B deposits $5,000 at the end of each year for 5 years. Interest is 4% compounded semiannually. What is the value of the deposits at the end of 5 years? a.$54,749

b.$27,082
c.$44,913
d.$22,259

User Ginge
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1 Answer

5 votes

Final answer:

Using the future value of an annuity formula, it's calculated that with an annual deposit of $5,000 and a 4% interest rate compounded semiannually over 5 years, Company B's deposits will be worth approximately $27,082.

Step-by-step explanation:

To determine the value of Company B deposits at the end of 5 years with an interest rate of 4% compounded semiannually, we need to calculate the future value of an annuity. The formula for finding the future value of an annuity compounded semiannually is given by:

FV = P × {[(1 + r/n)^(nt) - 1] / (r/n)}

Where:

  • FV is the future value of the annuity.
  • P is the periodic payment amount.
  • r is the annual interest rate (in decimal form).
  • n is the number of times the interest is compounded per year.
  • t is the number of years the money is deposited for.

For this problem:

  • P = $5,000 (the annual deposit)
  • r = 0.04 (4% annual interest rate)
  • n = 2 (since the interest is compounded semiannually)
  • t = 5 (the money is deposited over 5 years)

Substituting these values into the formula:

FV = 5000 × {[(1 + 0.04/2)^(2×5) - 1] / (0.04/2)}

Calculating the value inside the brackets:

FV = 5000 × {[(1 + 0.02)^(10) - 1] / 0.02} = 5000 × {[(1.02)^10 - 1] / 0.02}

Finally, calculating the future value gives:

FV ≈ $27,082

Therefore, the value of the deposits after 5 years is approximately $27,082, which corresponds to answer choice b.

User Stinkyfriend
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