Fixed Income - question related to Bond Duration understand, continuous, investment

Bluetick1010

Bond duration is defined as a measure of how long on average the holder of the bond has to wait before receiving cash payments. For a coupon paying bond, I understand this as at what point in entire tenure will I recover my investment. I referred to examples given in books and according to one of them:
consider a 3 Year 10% coupon bond with face value of $100. Suppose that the yeild is 12% per annum with continuous compounding. On computing using Macaulay’s method, I can see that the duration for this bond is 2.653 years. The bond price (computed by summing all cash flows discounted using the yield %) is $94.213.
Now my question is I am not able to prove it mathematically that in 2.653 years I am able to recover 94.213 given all above conditions.
can someone please help?