Discover offers a home equity line of credit that lowers the total of the monthly payments on several

hypothetical loans by $$366\mathrm{.}12.($See the following table.$)$

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.

$($a$)$ Using this interest rate and monthly payments for the $10$ years, how much money will still be owed at the

end of the $10$ years?

$($b$)$ How much is paid during the $10$ years?

$($c$)$ How much would the payment have to be for the debt to be paid in the $10$ years?

$($d$)$ How long would it take to pay off the debts under the original plan if interest were $15\%$ on each loan?

$\backslash$table$[[$Loan Type,$\backslash$table$[[$Current Monthly Payment$],[$Example$]],$Discover Home Equity$],[$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,$PAID OFF,NONE$],[$Department store cards,$$2,500,$$$78\mathrm{.}63,$PAID OFF,NONE$],[\backslash$table$[[$Discover home equity line$],[$of credit$]],,,$$$25,000,$$$218\mathrm{.}54],[$Total$,$$$25,000,$$$584\mathrm{.}66,$$$25,000,$$$218\mathrm{.}54]]$