A student desired to invest $1,540 into an investment at 9% compounded semiannually for 6 years. With all else equal, what is the future value of this initial investment after the six year period

Answer:The future value of this initial investment after the six year period is $2611.6552Step-by-step explanation:Consider the provided information.A student desired to invest $1,540 into an investment at 9% compounded semiannually for 6 years. Future value of an investment: [tex]FV=P(1+r)^n[/tex]Where Fv is the future value, p is the present value, r is the rate and n is the number of compounding periods.9% compounded semiannually for 6 years.Therefore, the value of r is: [tex]r=\frac{0.09}{2}=0.045[/tex]Number of periods are: 2 × 6 = 12Now substitute the respective values in the above formula.[tex]FV=1540(1+0.045)^{12}[/tex][tex]FV=1540(1.045)^{12}[/tex][tex]FV=1540(1.69588)[/tex][tex]FV=2611.6552[/tex]Hence, the future value of this initial investment after the six year period is $2611.6552