Question

Find the present value of an annuity of $8000 paid at the end of each 6-month period for 4 years if the interest rate is 4%, compounded semiannually. (Round your answer to the nearest cent.)
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Answer 1

Compute the semi-annual interest rate, using the equation as shown below:

Semi-annual rate = Annual rate/ 2

                            = 4%/ 2

                            = 2%

Hence, the semi-annual rate is 2%.

Compute the present value annuity factor (PVIFA), using the equation as shown below:

PVIFA = {1 – (1 + Rate)^-Number of periods}/ Rate

                   = {1 – (1 + 0.02)^-8}/ 2%

             = 7.32548144028

Hence, the present value annuity factor is 7.32548144028.

Compute the present value of annuity, using the equation as shown below:

Present value = Semi-annual payment*PVIFA

                      = $8,000*7.32548144028

                     = $58,603.8515222

Hence, the present value of annuity is $58,603.85