City bank has six-year zero coupon bonds with a total face value of $20 million. The current market yield on the bonds is 10 percent.
-What is the modified duration of these bonds?

Question

Quizplus · Accepted Answer

Modified duration = Macaulay duration / (1 + y/n)
where y = yield and n = number of coupon payments per year.

Since these are zero coupon bonds, there are no coupon payments, so n = 1.

The Macaulay duration of a zero coupon bond is equal to its maturity, which is 6 years in this case.

Thus, modified duration = 6 / (1 + 0.10/1) = 5.45 years.

City Bank Has Six-Year Zero Coupon Bonds with a Total