Karou is considering different options for financing the $$$$14,000$ balance on her planned new car purchase. The cheapest advertised rate among the local banks is $6\mathrm{.}5$ percent for a $48-$month car loan. The current rate on her revolving home equity line is $8\mathrm{.}5$ percent. Karou is in the $25$ percent federal tax bracket and the $5\mathrm{.}75$ percent state tax bracket.

a$.$ Calculate$$ Karou's monthly car payment using your financial calculator. Compare the payment amount if she uses the $48-$month car loan through her local bank versus her home equity line of credit. Assume both loans will amortize over $48$months$,$ and use the simple interest method.

b$.$ What are$$ Karou's income tax savings over the life of the loan if she chooses to use her home equity line of credit to finance the purchase of her new$$ car?

c$.$ Which loan offers the lower$$ payment? Which loan has the lower$$ after$-$tax cost? Use this information to determine which loan she should choose.

d$.$ In a discussion with her father about financing her new$$ car, Karou was surprised to hear that he once financed a car with the$$ add$-$on method of interest calculation. He planned to repay the $$$$1,800$ loan within $1$ year but was able to do so after $9$ months because of a bonus he earned at work. The interest rate was $5\mathrm{.}5$ percent. Calculate the monthly$$ payments, as well as the final payment to pay off the loan. How much interest was$$ "saved" or$$ rebated, using this method of financing and the rule of$78$s$?$