Federal officials today said more than 100,000 permanent loan modifications have been approved so far under their Making Home Affordable Program, designed to offer up to 4 million homeowners reduced monthly payments.

That number of approved loan workouts breaks down to about 66,000 that have accepted and about 34,000 that have not signed the deals, according to the Treasury Department and Department of Housing and Urban Development.

Also, the median reduction of monthly payments is more than $500, federal officials said, and about 850,000 borrowers have had their payments lowered by at least that amount.

Officials said the number of permanent modifications is a “significant acceleration” compared to months ago, when lenders and loan servicers were chastised by the Obama administration for being slow in helping borrowers.

The modifications can include lower interest rates, stretching payments to 40 years and forgiving part of the principal.

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The permanent loan changes come after what’s supposed to be a three-month trial period in which the borrowers demonstrate they can make the new payments on time. If not, they don’t get permanent modifications.

But Long Island borrowers in the program and nonprofit housing advocates said the trial periods often stretch past three months and the permanent modifications are always not the same as the terms in the trial period. The federal program calls for the permanent modifications to be same as the trial period.