Dr$.$ & Mr$.$ Baker were delighted to find a house for sale that they loved which required them to borrow $$140,000.$ They need to decide between a $20-$year or $30-$year loan. Both loans charge interest at a rate of $9\mathrm{.}6\%$ per year compounded monthFind the total amount paid over the life of the $20-$year loan.

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$($e$.)$ Find the total amount paid over the life of the $30-$year loan.

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$($f$.)$ Find the total savings by going with the $20-$year loan.