Question

What is the duration of a three-year Treasury bond with a 13 percent semiannual coupon selling at par

Answer 1

the formula to calculate modified duration of bonds:

modified duration = [1 - (1 + y)⁻ⁿ] / y

since this bond pays semiannual interest,

modified duration = [1 - (1 + 6.5%)⁻⁶] / 6.5%

modified duration = (1 - 1.065⁻⁶) / 6.5% = 4.841 semiannual periods

modified duration in years = 4.841 / 2 = 2.4205 years

if you want to determine the Macaulay duration = modified duration x (1 + yield) = 2.4205 years x 1.065 = 2.5778 years