Rental Expenses - Depreciation of Mortgage Costs - Refinance Scenario

A simplified scenario to help get my question across:

- I currently depreciate my closing costs for my rental property when I purchased it

- I depreciated costs over 30 years, the term of my original loan. 

- Assume original costs were $5000

- Assume last year was 15th year, meaning I have depreciated $2500 and have $2500 left to depreciate over the remaining 15 years.

 

If I refinance this year (30yr) and incur closing costs of say $3000, for my current tax year:

- Do I recoup the remaining $2500 cost as a straight expense (not depreciated) from the original loan and then set up another 30 yr depreciation schedule for the refinanced costs?  Or must I maintain two depreciation schedules for the two different costs?

 

I guess this question can go for any depreciated asset like a car/fridge etc. that we get rid of prior to it it being fully depreciated.