Find the present value of an ordinary annuity of $1,400 payments each made semiannually over 8 years and earning interest at 12% per year compounded semi-annually.
We can use the present value formula for an ordinary annuity:
PV = P * ((1 - (1+r)^(-n))/r)
Where PV is the present value, P is the payment amount, r is the interest rate per period, and n is the total number of payment periods.
In this case, P = $1,400, r = 0.06 (12% per year compounded semi-annually), and n = 16 (8 years x 2 payments per year).
PV = $1,400 * ((1 - (1+0.06)^(-16))/0.06)
PV = $1,400 * ((1 - 0.38843)/0.06)
PV = $1,400 * (11.04118)
PV = $15,457.63
Therefore, the present value of the annuity is $15,457.63.