A 20-year bond with a $1 000 face value was issued with a yield to maturity of 4.5% and pays coupons semi-annually. After 10 years, the yield to maturity is still 4.5% and the clean price of the bond is $960.09. After three more months go by, what would you expect the dirty price to be?

Question

Quizplus · Accepted Answer

Since the yield to maturity is constant, changes in price are due to the passage of time and the accumulation of interest. In three more months, the bond will have accrued three more months of interest, which will increase the dirty price. However, since the yield to maturity has not changed, the increase in price due to accrued interest will be offset by a decrease in price due to the passage of time. Therefore, the dirty price after three more months will be slightly higher than the current clean price of $960.09, but lower than the current dirty price. Only one answer choice is slightly higher than the current clean price, which is answer B) $970.09.

A 20-Year Bond with a $1 000 Face Value Was