You have just purchased a car and taken out a $ $45,000$ loan. The loan has a$$ five$-$year term with monthly payments and an APR of $6\mathrm{.}4\%.$

a$.$ How much will you pay in$$ interest, and how much will you pay in$$ principal, during the first$$ month, second$$ month, and first$$ year? $($Hint: Compute the loan balance after one$$ month, two$$ months, and one$$ year.$)$

b$.$ How much will you pay in$$ interest, and how much will you pay in$$ principal, during the fourth year$($i$.$e$.,$ between three and four years from$$ now$)?$

$($Note: Be careful not to round any intermediate steps less than six decimal$$ places$)$