The present value of the annuity is calculated to be $41,221.185 if it pays $5,000 at the end of each 6-month period for 7 years.
The formula for determining the present value of an annuity is
PV = PMT × [1 - (1 / 1+r)^n] / r]
Here PMT represents the Dollar amount of each payment, r represents the interest rate, and n represents the number of periods in which payments will be made.
Since the payment is at the end of each 6-month period for 7 years and the interest rate is 8% compounded semiannually therefore the number of periods in which payments will be made is equal to 7 × 2 = 14
Now substituting the values to determine the present value as follows;
PV = 5000 × [1 - (1 / 1 + 0.08)^14 / 0.08]
PV = 5000 × [1 - (1 / 1.08)^14 / 0.08]
PV = $41,221.185
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