Question

Find the present value of an annuity with payments of $2,000 at the end of every six months for 8 years. The interest rate is 8% compounded semi-annually. The present value of the annuity is $ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Answer 1

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).