Mail Solicitation Home Equity Loan: Is This a Good Deal?

Discover offers a home equity line of credit that lowers the total of the monthly payments on several hypothetical loans by $$366\mathrm{.}07.($See the following table.$)$

The home equity loan payment is based on $"10\mathrm{.}49\%$ APR annualized over a $10-$year term." This means that the loan is amortized at $10\mathrm{.}49\%$ with monthly payments.

Table $1+$

$\backslash$table$[[$Loan Type,$\backslash$table$[[$Current Monthly$],[$Payment Example$]],\backslash$table$[[$Discover Home$],[$Equity$]]],[\backslash$table$[[$Loan$],[$Amount$]],\backslash$table$[[$Monthly$],[$Payment$]],\backslash$table$[[$Loan$],[$Amount$]],\backslash$table$[[$Monthly$],[$Payment$]]],[$Bank cards,$$10,000,$$$186\mathrm{.}00,$PAID OFF,NONE$],[$Auto loan,$$12,500,$$$320\mathrm{.}03,$PAID OFF,NONE$],[\backslash$table$[[$Department$],[$store cards$]],$$$2,500,$$$78\mathrm{.}58,$PAID OFF,NONE$],[\backslash$table$[[$Discover home$],[$equity line of$],[$credit$]],,,$$$25,000,$$$218\mathrm{.}54$