You have just purchased a car and taken out a $$41,000$ 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.$)$

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.$)$

During the first month, you will pay $ in principal. $($Round to the nearest cent.$)$