Question

A bond has a YTM of 6.5%, a modified duration of 16.9 years, a duration of 18 years and a 30 year maturity. By what percentage will the bond's price change if market interest rates increase by 0.75%? A. 12.675 B. -12.675 C. .750 please show work

Answer 1

To calculate the percentage change in the bond's price when market interest rates increase by 0.75%, you can use the modified duration. The formula for percentage price change is as follows:

Percentage Price Change = -Modified Duration × Change in Yield

Where:

- Modified Duration is given as 16.9 years.

- Change in Yield is the increase in market interest rates, which is 0.75% or 0.0075 in decimal form (since it's an increase, it's negative for bond prices).

Now, plug these values into the formula:

Percentage Price Change = -16.9 × (-0.0075)

Percentage Price Change = 0.12675

To express this as a percentage, multiply by 100:

Percentage Price Change = 0.12675 × 100 = 12.675%

So, the bond's price will change by approximately 12.675% if market interest rates increase by 0.75%. Therefore, the correct answer is A. 12.675%.

Step-by-step explanation: