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Default Depreciation of assets - no. of yrs required

Kindly tell me whether there is any formula or readymade function to find out
the number of years required to depreciate an asset fully ( minimum value $
1)using a declining balance method. For example, if my asset is worth $ 1000
now and it has to be depreciated at 10% / year i.e., value at the end of the
1st yr would be $900, second yr $810 and so on. I want the year to be
calculated until the value becomes $1 . The minimum depreciation during any
year should be $1 i.e., if it happens that in any year the depreciation will
be less $ 1 , the minimum depreciation to be provided would be $1 so as to
reach balance asset value of $1. I could arrive at the value using a table.
But I am looking for a short cut.
 
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