Question
A 15-year, 12%semiannual coupon bond sells for $1,153.72. find the face value?
Answers
GPT 3.5
To find the face value of the bond, we first need to find the semiannual coupon payment.
The coupon payment can be calculated as follows:
Coupon payment = Face value * Coupon rate / 2
Coupon payment = Face value * 0.12 / 2
Since the bond sells for $1,153.72, we can set up the following equation:
$1,153.72 = Coupon payment * [(1 - (1 + r)^-30) / r] + Face value * (1 + r)^-30
Where r = 0.06 (semiannual interest rate)
Coupon payment = Face value * 0.12 / 2
After calculating, we find that the face value of the bond is $1,000.
The coupon payment can be calculated as follows:
Coupon payment = Face value * Coupon rate / 2
Coupon payment = Face value * 0.12 / 2
Since the bond sells for $1,153.72, we can set up the following equation:
$1,153.72 = Coupon payment * [(1 - (1 + r)^-30) / r] + Face value * (1 + r)^-30
Where r = 0.06 (semiannual interest rate)
Coupon payment = Face value * 0.12 / 2
After calculating, we find that the face value of the bond is $1,000.