Reducing balance asset - get back to purchase date

Hi i am trying to get back to the original purchase date of an asset.

It has being depreciating using the reducing balance method.

I have the Net book value of the asset currently, the original cost and the depreciation rate.

However i do not know the quickest way in excel to work back to the original purchase date.

See attached file for examples and my long workaround to estimate purchase date.
Thanks for any assistance

Reducing Bal assets.xlsx

hi dear
welcome to forum,
are u looking for this sol?

refer attachment plz