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Thirty percent of households 80 and older pay more than they can afford for housing.

Owning a home with no mortgage is probably the best way to ensure a long-term financially secure retirement, according to a new report on housing and financial security by the Joint Center for Housing Studies at Harvard University.

The report observes that keeping a roof over their heads is the biggest expense in most people’s retirement budgets. One-third of adults age 50 and older pay what the Harvard housing experts consider an “excessive share” of their incomes for housing. Because most people’s income decreases as they age, 37 percent of households age 80 and older are paying more than they can afford for housing. Some 20 percent are paying much more than they can afford, according to the study.

Older renters are the most likely to be burdened by housing costs, points out Jennifer Molinsky, a research associate at the center and author of the paper. As they age, their incomes don’t keep up with rising rents, so as many as 60 percent are struggling by the time they are age 80. People who own their own homes can be in the same or worse shape if they haven’t paid off their mortgages.

The winners are people who are able to enter retirement with no mortgage.  On average, the monthly housing cost for those with no mortgage — including property taxes, insurance and utilities — is less than a third of what it is for older owners with mortgages and less than half of what renters pay, the study found.

There are also other good reasons to pay off your mortgage before you hang up your work boots, Molinsky says.

Mortgage-free homeowners are wealthier. Homeowners aged 50 and over are three times more likely to own stocks, bonds and other investments compared to renters. The sooner you pay off the mortgage, the more opportunity you have to invest.

Owners with no mortgage can take out a reverse mortgage. If you own a home free and clear and face unexpected expenses, you can turn to a reverse mortgage to get your retirement budget back on track.

Long-term care is more affordable. The median net worth of an over-50 homeowner with no mortgage is 44 times the net wealth of the median over-50 renter. Molinsky calculates that taking home equity into account, the average homeowner with no mortgage can afford 42 months of nursing home care. People who own their own homes also have greater flexibility if they want to modify their homes to accommodate caregiving.

Retirees don’t move. Some people argue against home ownership  for older people on the grounds that selling their homes could be difficult, but Molinksy says that not only is it hard to predict whether a house will sell down the road, in all likelihood, the average retiree or soon-to-be retiree won’t want to sell for another two decades. “People are making housing decisions in their 60s that will affect them for 20 or 30 years,” she says. “The house you have now is probably the house you will have forever.”

Here are more reasons why some retirees are so much better off than others.

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