Question

Use the compound interest formulas A = P 1+ and A= Pe" to solve the problem given Round answers to the nearest cent Find the accumulated value of an investment of $15,000 for 7 years at an interest rate of 4 5% if the money is a. compounded semiannually. b. compounded quarterly c compounded monthly, d. compounded continuously a. What is the accumulated value if the money is compounded semiannually? (Round your answer to the nearest cent. Do not include the $ symbol in your answer.) ​

Answer 1

The accumulated value of a $15,000 investment over 7 years at a 4.5% interest rate compounded semiannually is approximately $20,671.35.

Step-by-step explanation:

The student's question involves calculating the accumulated value of a $15,000 investment over 7 years at a 4.5% interest rate with the money being compounded semiannually. To find the accumulated value, we use the compound interest formula A = P(1 + r/n)^(nt). In this case, the values are P = $15,000, r = 0.045 (since 4.5% as a decimal is 0.045), n = 2 (since the interest is compounded semiannually), and t = 7 years.

The calculation steps are as follows:

1. 
   
3. Convert the interest rate from a percentage to a decimal: r = 4.5% or 0.045.
4. 
   
6. Determine the number of times the interest is compounded per year: n = 2 for semiannual compounding.
7. 
   
9. Substitute the values into the formula: A = 15000(1 + 0.045/2)^(2*7).
10. 
    
12. Calculate the compound interest: A = 15000(1 + 0.0225)^(14).
13. 
    
15. Compute the result: A ≈ 15000(1.0225)^14 ≈ 15000(1.37809) ≈ $20671.35.

Therefore, the accumulated value of the investment when compounded semiannually is approximately $20,671.35.