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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