A $1000 bond with coupons at j₂ = 8% is purchased to yield j₂ = 7%.The write down in the first period after purchase is $4.01.What is the purchase price of the bond?

Question

Quizplus · Accepted Answer

The purchase price of the bond can be calculated using the formula for the present value of a bond, which is the sum of the present value of the coupons and the present value of the face value. Given the bond has an 8% coupon rate, is purchased to yield 7%, and experiences a write-down of $4.01 in the first period, we can infer that the bond was purchased at a premium because its coupon rate is higher than the yield rate. The write-down indicates the amortization of the premium over the first period. Without the exact number of periods until maturity, we cannot directly calculate the purchase price from the information given. However, the correct answer must account for the bond being purchased at a price above its face value ($1000) due to the higher coupon rate compared to the yield, and then adjusted for the premium amortization. Among the provided options, $1028.29 is the only one that suggests a premium was paid for the bond, aligning with the given conditions.

A $1000 Bond with Coupons at J2 = 8% Is

A $1000 Bond with Coupons at J₂ = 8% Is