In this assignment, you will apply your newly$-$gained knowledge of exponential functions and compound interest and apply it to a real$-$world scenario, paying back student loans. It is estimated that over $60\%$ of students graduating from college leave with student loan debt. It is a very common scenario for many students and, therefore, a relevant one for many of you as you think about your options for continuing your education after high school. Here is the scenario for this assignment:

Penny attended a four$-$year state college. She took out a student loan to pay for her tuition and room & board for the four years she was attending college. Her tuition fees were $$6,970$ per year, and her room and board cost was $$11,320$ per year. Now that she has graduated, she must start paying back her loan. Fortunately, Penny has a grace period of one year before she has to start paying back the loan. Her loan details are as follows:

There is a fixed$-$rate interest of $4\mathrm{.}5\%,$ and the interest compounds each month.

During her one$-$year grace period, interest will accrue on the loan so that when she has to start paying the loan back, she will owe more than she owes now.

Her goal is to be able to pay off the loan in $10$ years.

Given all of this information, answer the following questions:

What is the original loan amount, i$.$e$.,$ how much were the total costs for tuition plus room & board for the four years that Penny attended the college?

What is the new loan amount after the one$-$year grace period $($remember that interest will accrue on the loan during this initial $12-$month period that she is not paying anything back on the loan$)?$ This is the amount she will be responsible for paying back. $($Round your answer to the nearest whole dollar.$)$ Hint: Use A$=$ P$(1+$r$/$n$)^($nt$)$ to solve problem $2.$

Given that she can pay back the loan in full after $10$ years of payments,

What is the total amount she will end up paying back $($both principal and interest that has accrued over the $10$ years$)?$

How much will her monthly payments on the loan be for those $10$ years? $($Round your answers to the nearest whole dollar.$)$ Hint: Use A$=$ P$(1+$r$/$n$)^($nt$)$ to solve problem $3,$ part $1.$ Take the total owed and divide by the number of payments to find the monthly payment.