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 7.0 % ​(annual payments). The yield to maturity on this bond when it was issued was 6.0 %. What was the price of this bond when it was​ issued?

Answer 1

$1,073.60

Step-by-step explanation:

bond's current price = PV of face value + PV of coupons

maturity = 10 years

face value = $1,000

coupon rate = 7% annual

market rate = 6%

PV of face value = $1,000 / (1 + 6%)¹⁰ =$558.39

PV of coupons = coupon x annuity factor (10 years, 6%) = $70 x 7.3601 = $515.21

market value at issue date = $558.39 + $515.21 = $1,073.60

since the bond's coupon rate was higher than the market rate, the bond was sold at a premium.