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Part $1$

$$After$-$tax cost of debt$$Personal Finance Problem$$Bella Wans is interested in buying a new motorcycle. She has decided to borrow the money to pay the $$$$20$ comma $000$

purchase price of the bike. She is in the $35$

$\%$

income tax bracket. She can either borrow the money at an interest rate of $4$

$\%$

from the motorcycle$$ dealer, or she could take out a second mortgage on her home. That mortgage would come with an interest rate of $6$

$\%.$

Interest payments on the mortgage would be tax deductible for$$ Bella, but interest payments on the loan from the motorcycle dealer could not be deducted on$$ Bella's federal tax return.

a$.$Calculate the $$after$-$tax cost of borrowing from the motorcycle dealership.

b$.$ Calculate the $$after$-$tax cost of borrowing through a second mortgage on$$ Bella's home.

c$.$Which source of borrowing is less costly for$$ Bella?

d$.$Should Bella consider any other factors when deciding which loan to take$$ out?