Karou is considering different options for financing the

$$$$12$ comma $000$

balance on her planned new car purchase. The cheapest advertised rate among the local banks is

$6\mathrm{.}75$

percent for a

$48$

$-$month

car loan. The current rate on her revolving home equity line is

$9$

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

$$$$2$ comma $200$

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

$5\mathrm{.}75$

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$?$

e$.$ Assume$$ Karou's father could finance

$$$$2$ comma $200$

today at

$5\mathrm{.}75$

percent using the simple interest method of calculation. How much would the payments$$ be$?$ Calculate the final payment to pay off the loan in

$9$

months. How much interest was$$ "saved"?

f$.$ Considering the information in parts

$($d$)$

and

$($e$),$

calculate the difference in finance charges assuming neither loan was paid off early.

g$.$ Assuming Karou did not have access to a home equity$$ line, what factors might she consider to reduce the$$ lender's risk and therefore$$ "buy" herself a$$ lower$-$cost loan? $($Hint: Consider Principle$8$: Risk and return go hand in$$ hand.$)$

h$.$ What is the collateral for each of the loans Karou is$$ considering? If the bank repossessed her$$ car, would she still have to repay her$$ loan?