The Mendez family is considering a mortgage loan of $$348,500$ at an annual interest rate of $6\mathrm{.}7\%.$

$($a$)$ How much greater is their mortgage payment if the term is $20$ years rather than $30$ years?

$($b$)$ How much less is the amount of interest paid over the life of the $20-$year loan than over the life of the loan?

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