One Month Rent for Free

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My husband threw this idea at me: What if we charge the tenants a little more for rent each month and gave them the 12th month for free? Here's how it would work:

If rent is normally $900 per month, we charge them $982 per month for 11 months. This is the same as if $900 were paid for 12 months. We tell the tenant that if they pay their rent on time every single month for 11 months, then they can have the last month for free. If they make all their payments on time, then we make the exact same amount we would have anyway. If they don't make all payments on time, then we just made an extra month's worth of rent, because they would have to pay the 12th month. The tenant doesn't have to know that we are charging more than we normally would have.

Of course it would only work if people are willing to pay $82 more per month. Seems to me like they would be thrilled to get a free month's worth of rent.

I've been mulling it over. What do you think? Pros and cons?