Bond duration closed form formula

Bond duration closed-form formula:

D u r = C ( 1 + a i ) ( 1 + i ) m − ( 1 + i ) − ( m − 1 + a ) i i 2 ( 1 + i ) ( m − 1 + a ) + 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