To calculate the future value of an investment with compound interest, we can use the formula:
Future Value = Principal Amount × (1 + (Interest Rate / Number of Compounding Periods))^(Number of Compounding Periods × Number of Years)
In this case, the principal amount is $1,540, the interest rate is 9% (0.09 as a decimal), and the investment is compounded semiannually (twice a year) for 6 years.
Plugging in the values:
Future Value = $1,540 × (1 + (0.09 / 2))^(2 × 6)
After doing the calculations, the future value of this initial investment after the six-year period would be approximately $2,638.33.
So, the investment would grow to around $2,638.33 over the six-year period.