To calculate the future value of the investment when $24,000 is deposited into an account earning 4% annual interest compounded semiannually for 15 years, you can use the formula for compound interest:
\(A = P \times (1 + \frac{r}{n})^{nt}\)
Where:
- \(A\) is the future value of the investment
- \(P\) is the principal amount (initial deposit) = $24,000
- \(r\) is the annual interest rate = 4% or 0.04
- \(n\) is the number of times the interest is compounded per year = 2 (semiannually)
- \(t\) is the number of years the money is invested for = 15
Plugging in the values:
\(A = 24000 \times (1 + \frac{0.04}{2})^{2 \times 15}\)
Calculate the values inside the parentheses first:
\(1 + \frac{0.04}{2} = 1.02\)
Then calculate the exponent:
\(2 \times 15 = 30\)
Substitute the values back into the formula:
\(A = 24000 \times 1.02^{30}\)
Now, calculate \(1.02^{30}\) to find the future value of the investment after 15 years with semiannual compounding.
Once you have the result, round it to the nearest cent to provide the accurate future value of the investment.
