Question

Find the present value (in dollars) of an annuity that pays $4,000 at the end of each 6-month period for 8 years if the interest rate is 4% compounded semiannually. (Round your answer to two decimal places.)

Answer 1

Present value of annuity = P * [( 1 - ( 1+R)^-N) / R

Where, P = Payment

R = Rate of interest per period

N = Number of periods

= 4000 * [( 1 - ( 1 +(4%/2))^-(8*2)] / (4%/2)

= 4000 * [( 1 - ( 1 +2%)^-16] / 2%

= 4000 * [( 1 - 0.72844581371) / 0.02]

= 4000 * 13.5777093

= 54310.8372

So, The present value of annuity is 54310.8372