Question: Question: Find a formula for the modified duration and convexity of a zero coupon bond maturing T years from today, assuming an interest rate r

Question: Find a formula for the modified duration and convexity of a zero coupon bond maturing T years from today, assuming an interest rate r compounding continuously.

I have read that If a bond is continuously compounded, the Modified duration of the bond equals the Macaulay duration.

So i feel like I need to prove:

If a bond is continuously compounded, the Modified duration of the bond equals the Macaulay duration

Please show all steps, thank you!

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