What is the percentage price change for the bond if interest rates decline 50 basis points from the original 5 percent?
A)-2.106 percent.
B)+2.579 percent.
C)+0.000 percent.
D)+3.739 percent.

Question

Quizplus · Accepted Answer

Percent change in price in  rates decrease from 5.0 percent to 4.5 percent11efb86c_469a_9852_9137_79f57b43d027_TB1314_00 
 Percent ∆P = (P1 - P0) ÷ P0
 %∆P = (102,578.94 - 100,000) ÷ 100,000 = +0.025789. To calculate the percentage price change for the bond, we can use the following formula:
Percentage price change = - Modified duration x Change in interest rates
Since the bond has a duration of 15.87, we can calculate:
Percentage price change = - 15.87 x (-0.50%) = 7.935%
However, we need to remember that the bond's price has an inverse relationship with interest rates, which means that as interest rates decline, the bond's price will increase. Therefore, the correct percentage price change for the bond is:
Percentage price change = - 7.935% = +2.579% (rounded to three decimal places)
So, the best choice is B because it correctly calculates the percentage price change for the bond if interest rates decline 50 basis points from the original 5 percent.

What Is the Percentage Price Change for the Bond If