what is the present value of the following annuity What is t

What is the present value of the following annuity? $987 every half year at the end of the period for the next 7 years, discounted back to the present at 4.98 percent per year, compounded semiannually. Round the answer to two decimal places

Solution

Amount of payment at the end of every six months = $987

Number of payments in 7 years = 7* 2 = 14

Semi-annual rate of interest = 4.98%/2 = 2.49% = 0.0249

Present value of annuity = Annuity amount * {1-(1+r)^-n}/r

Present value of this annuity = $987 * (1-1.0249^-14)/0.0249 = $11,546.93

Hence, correct answer is $11,546.93