Suppose you take out a five$-$year car loan for $$13000,$ paying an annual interest rate of $5\%.$ You make monthly payments of $$245$ for this loan.

Getting started $($month $0)$: Here is how the process works. When you buy the car, right at month $0,$ you owe the full $$13000.$ Applying the $5\%$ interest to this $(5\%$ is $"5$ per $$100"$ or $"0\mathrm{.}05$ per $$1"),$ you would owe ${0\mathrm{.}05}^{***}$$$13000=$$$650$ for the year. Since this is a monthly loan, we divide this by $12$ to find the interest payment of $$54\mathrm{.}17$ for the month. You pay $$245$ for the month, so $$54\mathrm{.}17$ of your payment goes toward interest $($and is never seen again...$),$ and $)=$$$190\mathrm{.}83$ pays down your loan.

$($Month $1)$: You just paid down $$190\mathrm{.}83$ off your loan, so you now owe $$12809\mathrm{.}17$ for the car. Using a similar process, you would owe ${0\mathrm{.}05}^{***}$$$12809\mathrm{.}17=$$$640\mathrm{.}46$ for the year, so $($dividing by $12),$ you owe $$53\mathrm{.}37$ in interest for the month. This means that of your $$245$ monthly payment, $$53\mathrm{.}37$ goes toward interest and $$191\mathrm{.}63$ pays down your loan.

The values from above are included in the table. Continue the process for the rest of the first year of the loan.

$\backslash$table$[[$Months$,$Amount still owed,$\backslash$table$[[$Monthly interest$],[$paid$]],\backslash$table$[[$Amount of monthly$],[$payment that goes$],[$toward paying off$],[$the loan $($after$],[$paying interest$)]]],[0,13000,54\mathrm{.}17,190\mathrm{.}83],[1,12809\mathrm{.}17,53\mathrm{.}37,191\mathrm{.}63],[2,12617\mathrm{.}54,,],[3,,,],[4,,,],[5,,,],[6,,,],[7,,,],[8,,,],[9,,,],[10,,,],[11,,,],[12,,,]]$

What is the total amount paid in interest over this first year of the loan?