Question

The face value is​ $82,000, the stated rate is​ 10%, and the term of the bond is eight years. The bond pays interest semiannually. At the time of​ issue, the market rate is​ 8%. What is the present value of the bond at the issue​ date? Present value of​ $1: ​4% ​5% ​6% ​7% ​8% 15 0.555 0.481 0.417 0.362 0.315 16 0.534 0.458 0.394 0.339 0.292 17 0.513 0.436 0.371 0.317 0.270 18 0.494 0.416 0.350 0.296 0.250 19 0.475 0.396 0.331 0.277 0.232 Present value of ordinary annuity of​ $1: ​4% ​5% ​6% ​7% ​8% 15 11.118 10.380 9.712 9.108 8.559 16 11.652 10.838 10.106 9.447 8.851 17 12.166 11.274 10.477 9.763 9.122 18 12.659 11.690 10.828 10.059 9.372 19 13.134 12.085 11.158 10.336 9.604

Answer 1

$91,561.20

Step-by-step explanation:

bonds face value $82,000

coupon rate 10%, 5% semiannual

periods 8 x 2 = 16

market price:

PV of face value = $82,000 x 0.534 (PV factor, 4%, 16 periods) = $43,788

PV of coupon payments = $4,100 x 11.652 (PV annuity factor, 4%, 16 periods) = $47,773.20

market price = $43,788 + $47,773.20 = $91,561.20