Given data:
PMT = $7,500
Interest rate = 4% or 0.04
Compounded semiannually = twice per year
Time = 2 years
Number of periods in total = 2 years x twice per year = 4 periods
interest rate per period = 0.04/2 = 0.02
The formula in getting the future value of an ordinary annuity is:
[tex]F=PMT(\frac{1+i)^n-1}{i})[/tex]where
i = interest rate per period
n = total number of periods
PMT = regular payment
From the given data above, let's substitute those in the formula.
[tex]\begin{gathered} F=7500\times\frac{(1+0.02)^4-1}{0.02} \\ F=7500\times\frac{1.02^4-1}{0.02} \\ F=7500\times\frac{0.08243216}{0.02} \\ F=7500\times4.121608 \\ F=30,912.06 \\ F\approx30,912.1 \end{gathered}[/tex]Ther
