Question

Suppose that General Motors Acceptance Corporation issued a bond with 10 years until​ maturity, a face value of $ 1 comma 000​, and a coupon rate of 7.5 % ​(annual payments). The yield to maturity on this bond when it was issued was 6.3 %. Assuming the yield to maturity remains​ constant, what is the price of the bond immediately before it makes its first coupon​ payment?

Answer 1

$1,159.22

Step-by-step explanation:

to determine the price of the bond immediately after it pays its first coupon:

YTM = {coupon rate + [(face value - market value)/n]} / [(face value + market value)/2]

0.063 = {75 + [(1,000 - market value)/9]} / [(1,000 + market value)/2]

0.0315 x (1,000 + x) = 75 + [(1,000 - x)/9]

31.5 + 0.0315x = 75 + 111.11 - 0.1111x

0.0315x + 0.1111x = 154.61

0.1426x = 154.61

x = 154.61 / 0.1426 = $1,084.22

the price of the bond immediately before it makes its first coupon payment = $1,084.22 + $75 = $1,159.22