Question

What is the duration of a four-year Treasury bond with a 10 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 + 5%)⁻⁸] / 5%

modified duration = (1 - 1.05⁻⁸) / 5% = 6.4632 semiannual periods

modified duration in years = 6.4632 / 2 = 3.2316 years

if you want to determine the Macaulay duration = modified duration x (1 + yield) = 3.2316 years x 1.05 = 3.39318 years