The already complex calculus on reverse mortgages is about to change. Reverse mortgages, which allow homeowners who are at least 62 years old to tap their home equity without making any mortgage payments, are typically used by borrowers who want to remain in their homes but need the money to pay off other debts. The vast majority of these mortgages are made through the Federal Housing Administration’s Home Equity Conversion Mortgage Program. Starting Monday, the program will introduce a reverse mortgage product known as the Saver, which will nearly eliminate one of the biggest upfront fees that borrowers are required to pay. But the program will also make changes in its standard reverse mortgages that will significantly increase certain costs but, in some cases, make more money available.