Answer:
The present value of the annuity is $28,171.97 (rounded to the nearest cent).
Explanation:
To calculate the present value of an annuity, we can use the formula:
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 periods.
In this case, the payment amount is $2,000, the interest rate is 8% compounded semi-annually, and the annuity lasts for 8 years (16 semi-annual periods).
First, we need to calculate the interest rate per period:
r = 8% / 2 = 0.08 / 2 = 0.04 (4% per semi-annual period).
Next, we can substitute the values into the formula and calculate the present value:
PV = 2000 * (1 - (1 + 0.04)^(-16)) / 0.04.
Using a calculator, the value of the expression inside the parentheses is approximately 0.563439.
PV = 2000 * 0.563439 / 0.04.
Calculating this, the present value of the annuity is approximately $28,171.97.
Therefore, the present value of the annuity is $28,171.97 (rounded to the nearest cent).