Russ and Roz Rosow have a ten$-$year$-$old loan with which they purchased their house. Their interest rate is

$105/8\%.$

Since they obtained this loan, interest rates have dropped, and they can now get a loan for

$91/4\%$ through their credit union. Because of this, the Rosows are considering refinancing their home. Each loan is a $30-$year simple interest amortized loan, and neither has a prepayment penalty. The existing loan is for $$114,000,$ and the new loan would be for the current amount due on the old loan. $($Round your answers to the nearest cent.$)$

$($a$)$ Find their monthly payment with the existing loan.

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$($b$)$ Find the loan amount for their new loan.

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$($c$)$ Find the monthly payment with their new loan.

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$($d$)$ Find the total interest they will pay if they do not get a new loan.

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$($e$)$ Find the total interest they will pay if they do get a new loan.

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$($f$)$ Should the Rosows refinance their home? Why or why not?

They should refinance. They will pay less interest with the new loan.

They should not refinance. They will pay less interest with the old loan.