Borrowing $$100$ from a friend

$\backslash$table$[[$Month$,\backslash$table$[[$Balance at$],[$the$],[$beginning of$],[$the month$]],$Interest,$\backslash$table$[[$Balance at$],[$the end of$],[$the month$]]],[1,100,,],[3,,,],[4,,,],[5,,,],[6,,,],[8,,,],[10,,,],[11,,,],[12,,,]]$

We change one detail in the example: you still borrow $$100$ from your friend; your friend still charges you $30\%$ in interest per year.

Now your friend wants to calculate the interest and add it to what you owe at the end of each MONTH $($instead of at the end of each year$).$

$($a$)$ There are $12$ months in a year. Determine the MONTHLYinterest rate and enter it below. $($Do not use a $\%$ symbol in your response.$)$

$($b$)$ Use the monthly interest rate you found in $($a$)$ to complete the table on the left. $($Use your calculator.$)$

$($c$)$ Look for a pattern. In words below, describe how to get from an entry in the last column to the entry directly below it$.$ Then use this pattern to guess the total amount you owe at the end of the thirteenth month.

$($Hint: look at your rough work to find the pattern; keep more than two decimal places in your calculations.$)$

You will use this pattern again later.