Bond duration closed-form formula

Bond duration closed-form formula:

$Dur={\frac {C{\frac {(1+ai)(1+i)^{m}-(1+i)-(m-1+a)i}{i^{2}(1+i)^{(m-1+a)}}}+{\frac {100(m-1+a)}{(1+i)^{(m-1+a)}}}}{P}}$

C = coupon payment per period (half-year)
P = present value (price)
i = discount rate per period (half-year)
a = fraction of a period remaining until next coupon payment
m = number of coupon dates until maturity

Look up Bond convexity closed-form formula

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