A bond has a duration of 7.5 years.Its current market price is $1,125.Interest rates in the market are 7 percent today.It has been forecasted that interest rates will rise to 9 percent over the next couple of weeks.How will the bond's price change in percentage terms?
A)The bond's price will rise by 2 percent.
B)The bond's price will fall by 2 percent.
C)The bond's price will fall by 14.02 percent.
D)The bond's price will rise by 14.02 percent.
E)The bond's price will not change.

Question

Quizplus · Accepted Answer

The bond's price will decrease due to the inverse relationship between bond prices and interest rates. Using the duration approximation formula for bond price change: ΔP/P = -D*(Δy/(1+y)), where ΔP/P is the percentage change in price, D is the duration (7.5 years), Δy is the change in yield (from 7% to 9%, or 2%), and y is the initial yield (7%). Plugging in the numbers: -7.5*(0.02/(1+0.07)) = -0.1402 or -14.02%.

A Bond Has a Duration of 7