Q: I signed an agreement to purchase my first home in November, and the deal closed a few days ago. Although the seller had paid this year’s property taxes in full, the closing statement shows that I had to pay $971 for part of the bill through my closing expenses. Did the closing agent screw up or, worse, try to rip me off?

A: No, it’s customary for the closing attorney or escrow officer who oversees a sale to pro-rate the property-tax bill and issue a credit to the seller. The credit is based on the amount of time the buyer and seller occupy the property during the county’s fiscal year.

Because your seller moved out before the fiscal year was up, he’s entitled to a pro-rated refund of the amount he prepaid. Your side of the closing statement will show that you were debited $971 for the taxes, and the seller’s side will show a $971 credit.

Since you didn’t write a check for your portion of the pro-rated tax bill, that statement is the only evidence that you paid your fair share of the property taxes.

That will come in handy if a problem arises with the assessor or tax collector, or if you deduct your share of the payment on your next federal income-tax return and get audited by the Internal Revenue Service.

Q: My brother and I own a duplex. I live in the front unit, and he lives in the back, but he wants to add another bedroom to his unit because he’s planning to get married and eventually have kids. My brother wants me to pay for half of the work because we will split the profits 50-50 when we sell, but I don’t think I should have to pay for the construction costs because I won’t have use of his new bedroom. What is a fair way to resolve this?

A: Perhaps the fairest way to resolve this dilemma is to ask your brother to pay for the new bedroom himself, but agree that he will be fully reimbursed for his outlays when the duplex is sold.

For example, if the new room costs $20,000 to build and the property is eventually sold for an $85,000 profit, the first $20,000 of the proceeds would go toward reimbursing your brother, and the remaining $65,000 would be split evenly between the two of you.

This isn’t a perfect solution, but it’s probably as close as you can get. If you adopt this plan, put it all down in writing before construction on the new bedroom begins.