A bond with 12 years to maturity has a 7 percent semiannual coupon and a face value of $1,000. (That is, the bond pays a $35 coupon every six months.) The bond currently sells for $1,000. What should be the price of a bond that pays a 7 percent annual coupon and has a face value of $1,000 with the same risk and maturity as the semiannual bond?
A) $970.16
B) $975.82
C) $981.34
D) $985.23
E) $990.33

Question

Quizplus · Accepted Answer

The bond that pays a 7 percent annual coupon and has the same risk and maturity as the semiannual bond should have a slightly lower price than the semiannual bond because it pays interest less frequently. However, since the semiannual bond is selling at its face value ($1,000) with a 7 percent semiannual coupon, implying a yield to maturity of 7 percent when compounded semiannually, the annual bond, to be equivalent, must offer a similar yield. Given the same yield, maturity, and risk, the difference in compounding frequency (annual versus semiannual) leads to a slight discount on the annual coupon bond to adjust for the less frequent interest payment, making $990.33 the closest and most reasonable choice among the options provided.

A Bond with 12 Years to Maturity Has a 7