Final answer:
Using the compound interest formula with the given values for principal amount, interest rate, compounding frequency, and time, the accumulated value of a $20,000 investment after 6 years at a 7% interest rate compounded semiannually is approximately $30,468.32.
Step-by-step explanation:
The problem asks us to find the accumulated value of an investment of $20,000 for 6 years at an interest rate of 7% compounded semiannually. To solve this, we can use the compound interest formula A = P(1 + r/n)^(nt), where:
- P is the principal amount ($20,000)
- r is the annual interest rate (0.07)
- n is the number of times the interest is compounded per year (2)
- t is the time the money is invested in years (6)
Plugging the values into the formula, we get:
A = 20000*(1 + 0.07/2)^(2*6)
A = 20000*(1 + 0.035)^(12)
A = 20000*(1.035)^12
Calculating using a calculator, we find:
A ≈ $30,468.32
Therefore, the accumulated value of the investment after 6 years is approximately $30,468.32, which corresponds to option D.