You want to buy a $$134,000$ home. You plan to pay $15\%$ as a down payment, and take out a $30$ year loan at $4\mathrm{.}35\%$ interest for the rest.

a$)$ How much is the loan amount going to be$?$

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b$)$ What will your monthly payments be$?$

c$)$ How much total interest do you pay?

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d$)$ Suppose you want to pay off the loan in $15$ years rather than $30.$ What will your monthly payment be$?$

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e$)$ How much money in interest will you save if you finance for $15$ years instead of $30$ years?