In my experience, most lenders will automatically apply any extra money as a principal reduction if you're "current" that month (ie, the normal monthly principal and interest payment has been made).As @John Horner suggested, it'd be best to talk to your lender directly to confirm what they do.Best wishes to you on your journey to real estate investing success!

Since this is a duplex, it may have unintended noise reduction qualities that will make for happier tenants. 

There are 4 ways to mitigate risk (risk avoidance, risk transfer, risk reduction and risk retention).

I would pay for it and then ask for a credit in that amount on the rent or ask for a reduction in rent until the amount you paid is recovered.

@Brian Eastman I know this is an old thread but if you are still reading this I have a couple question.While there is only a small reduction in year-to-year taxes, aren't there other benefits?

You can either structure the retainer off the total of the contract, or as a reduction of the final draw.

If we loose the property tax deduction, then what good are the rest of the tax reductions proposed?

Hopefully, the reduction of rental income by the operations entity's management fee could result in passive losses for the properties held by the holding series and parent LLC (all disregarded entities).  

Our average reduction rate is 35%-40% on our rental properties in Cleveland suburbs.

A house like that can be a great investment and the IRR comes from principal reduction and appreciation but not from the cash flow.