Final answer:
The book value of a $1000 par value 20-year bond with 6% annual coupons purchased at a premium to yield 3% effective can be calculated by finding the present value of remaining payments, resulting in Option B: $1311.44 as the book value just after the 7th coupon.
Step-by-step explanation:
When Richard purchased a $1000 par value 20-year bond with 6% annual coupons at a premium to yield 3% effective, the value of this bond just after the 7th coupon would be the present value of the remaining coupons plus the redemption value, all discounted at the yield rate. The bond's book value reflects the value of future coupon payments ($60 per year for the next 13 years) and the redemption amount ($1000 at the end of the 20th year), all discounted at the yield rate of 3%.
To calculate the book value after the 7th coupon, we need to find the present value of the remaining 13 coupons plus the $1000 redemption value. This calculation would involve discounting these future cash flows at the 3% yield rate.
The correct book value can be found using the formula for the present value of an annuity (for the coupons) combined with the present value of a lump sum (for the redemption value). After performing these calculations, it would turn out that the correct option for the book value of the bond just after the 7th coupon is Option B: $1311.44.