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$6.$ Jacquelin just found a great starter home for sale in her favorite neighborhood. She was able to negotiate a price of $$180,000$ for the home and plans to finance it through the credit union so that she can avoid PMI. The credit union is allowing Jacquelin to finance the whole amount with an interest rate of $7\mathrm{.}46\%$ for $30$ years.

a$)(3$ pts$)$ What will Jacquelin's monthly payment be$?$ $ $q,$

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b$)(2$ pts$)$ In total, how much will Jacquelin pay if she pays her loan off in $30$ years? $ Show your work. $$

c$)(2$ pts$)$ In total, how much will Jacquelin pay in interest? $

Show your work. $$