What is the modified duration of a four-year bond with annual 10% coupons and a 10% yield to maturity?

the formula to calculate modified duration of bonds:

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

modified duration = [1 - (1 + 10%)⁻⁴] / 10%  = 0.317 / 10% = 3.17 years

if you want to determine the Macaulay duration = modified duration x (1 + yield) = 3.17 years x 1.1 = 3.49 years

The modified duration shows how a bond's value can change as a result of a change in the interest rate.

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