Find the amount of an ordinary annuity for 6 years of semiannually payments of $1,400 that earn interest at 8%/year compounded semi-annually.
First, we need to determine the semiannual interest rate, which is half of the annual rate:
r = 8%/2 = 4% per six months
Next, we need to determine the total number of payment periods:
n = 6 years x 2 = 12 semiannual periods
Using the formula for the present value of an ordinary annuity:
PMT x ((1 - (1 + r)^-n) / r)
where PMT is the payment amount, r is the interest rate per period, and n is the total number of periods
We can substitute the given values and calculate the present value of the annuity:
1400 x ((1 - (1 + 4%)^-12) / 4%) = $13,843.81
Therefore, the amount of the ordinary annuity for 6 years of semiannually payments of $1,400 that earn interest at 8% per year compounded semi-annually is $13,843.81.