A new law has extended the valuable tax-credit program for first-time homebuyers, while also creating a new break for soldiers and other longtime homeowners who weren’t eligible for the credit under the previous Internal Revenue Service rules.

Several weeks ago, you wrote that Congress was probably going to extend the Nov. 30 expiration date for the $8,000 tax-credit program for first-time homebuyers. Since then, I heard a radio report that the extension was approved, but with “several modifications.” What are those changes?

The extension that Congress approved and President Barack Obama signed into law earlier this month changes several aspects of the program — all of which make millions of additional Americans eligible for the plan, even if they did not qualify under the previous guidelines.

Key improvements to the program include a provision that creates a new, $6,500 credit for most longtime homeowners who decide to buy a new house before the extended deadline of April 30, 2010. They also include an increase in the amount of money a taxpayer can earn while still claiming the valuable tax break, as well as more generous rules for members of the military.

Hundreds of readers have asked about the tax-credit program and the changes involved in the recent extension, so I’m devoting this column to answering some of the most common questions.

Q: What are the basic rules to claim the $8,000 first-time buyer’s credit?

A: You must not have owned a home for at least three years before the purchase. You cannot claim the deduction to purchase a vacation home or rental property, even if you have never owned a personal residence before.

In addition, you must be at least 18 and cannot be claimed as a dependent by any other taxpayer. You can’t claim the break if you buy a house or condominium from a relative, either.

Q: Are there limits on how much you can earn and still qualify for the credit?

A: Yes. You don’t qualify for the full $8,000 credit if you’re single and earn more than $125,000 per year, or if you’re married and your joint income tops $225,000.

A partial credit is available for those who make more, but it ends completely for singles who earn more than $145,000 annually and couples who make $245,000.

Nonetheless, that’s a boost over the previous limits, which capped the credit’s availability to single buyers who make more than $95,000 and married couples who earn more than $170,000.

Q: What would happen if I bought my first home today, claimed the credit, but sold it a year or two from now?

A: The Internal Revenue Service would likely demand that you pay some or all of the credit back if you sell within three years. You don’t have to worry about paying the money back if you remain in the new home longer.

Q: How does the new $6,500 credit for other buyers work?

A: The new credit, which was created earlier this month, is designed for those who want to buy another house but do not qualify for the $8,000 credit.

Under the new program, you can get up to $6,500 in credits if you have lived in your current home for at least five consecutive years of the past eight years and you sign a contract to purchase a new home by April 30, 2010. The deal must close by June 30.

Many of the same eligibility requirements that apply to the first-time buyer’s credit also apply to the new $6,500 credit program.

A key difference, though, is that you are ineligible if your adjusted household income tops $125,000 if you file taxes singly, or $225,000 if you file a joint return.

In addition, the property you purchase cannot cost more than $800,000, and you must move into the home as soon as the deal closes.

Q: We are retired, so we would like to sell our longtime home and then “trade-down” into a smaller, less-expensive property. Would we still qualify for the $6,500 tax credit?

A: Yes. There’s nothing in the new law that states the property you purchase must be worth more than the house you sell.

Q: I have owned and lived in my home for six years. Could I buy a new home, convert my current one into a rental, and still claim the $6,500 credit?

A: Sure, provided that you meet all of the program’s qualifications and move into the new home — thus making it your “personal residence” — as soon as the transaction closes.

Q: The extension of the program provides extra help to members of the military. How so?

A: First, an exemption has been carved out for soldiers who had to sell or stop using their home as a personal residence if their duty was extended or under other types of circumstances.

Those serving outside the U.S. will also get an extra year to claim the credit: The deadline for most of us is April 2010, but active-duty service personnel who are overseas generally have an extra 365 days until their eligibility for either the $8,000 or $6,500 tax credit expires.

Q: Where can I get more information?

A: Start by contacting your accountant, tax preparer or similar expert to discuss your current situation and home-buying plans.

Several Internet sites can help. They include the site operated by the Internal Revenue Service (irs.gov), as well as those run by the National Association of Realtors (realtor.org) and the National Association of Home Builders (federalhousingtaxcredit.com).