Suppose you borrow $$871,000$ to purchase a house. The loan term is $30$ years, the loan rate is $7\mathrm{.}39\%$ APR, and there are monthly payments.

Using this information, answer the following five questions below.

a$)$ Find the monthly payment on the original $30$ year loan. Express your answer as a positive number in dollars and cents, and round appropriately.

b$)$ Given the payment you found, above, find the total amount of interest that you will pay on the loan $("$assuming no pre$-$payment"$).$ Express your answer in dollars and cents.

c$)$ Now, assume you STOP paying anything on the loan between months $88$ and $115.$ Given this $($undesirable$)$ strategy, how much ADDITIONAL interest will you pay on the loan, compared to your answer to $($b$)?$ Per usual, express your answer in dollars and cents, and round appropriately. If your answer to this part is tESS than the answer to $($b$).$ express your answer as a negative number.

Hint: you make payment #$88.$

Hint $2$ : the term of the loan will extend beyond the original $360$ months.

Hint $3$: If the answer to $($b$)$ were $$400,000($it$\text{'}$s not...$).$ and the answer to this part were $$650,000($it$\text{'}$s not...$),$ then the answer you would enter below would be $$250,000($it won't...$).$d$)$ Now suppose you have a wealthy Aunt who gives vou a gift in month $100$ of the loan's life. The gift will allow you to pay the loan back according to the original $30$ year loan term. The terms of the gift are that you will receive it in month $100,$ and you must apply it $($i$.$e$.$ "pay it$")$ to the loan in one lump sum in month $100.$ In other words, everything happens in month $100.$ How much does your Aunt have to give you? Express your answer in dollars and cents.

Hint: you still make payment #$88.$

Hint $2$: NOT, the total term of the loan $($for everything....the entire loan...from start to finish... in totality$)$ is $360$ months.e$)$ Given your Aunt's gift, above, how much ADDITIONAL interest will you pay on the loan, compared to your answer to $($b$)?$ Per usual, express your answer in dollars and cents, and round appropriately. If your answer to this part is LESS than the answer to $($b$),$ express your answer as a negative number.

d$)$ Now suppose you have a wealthy Aunt who gives you a gift in month $100$ of the loan's life. The gift will allow you to pay the loan back according to the original $30$ year loan term. The term of the gift are that you will receive it in month $100,$ and you must apply it to the loan in one lump sum in month $100.$ In other words, everything happens in month $100.$ How much does your Aunt have to give you? Express your answer in dollars and cents.

e$)$ Given your Aunt's gift, above, how much ADDITIONAL interest will you pay on the loan, compared to your answer to $($b$)?$ Per usual, express your answer in dollars abd cents, and round appropriately. If your answer to this part is LESS than the answer to $($b$),$ express your answer as a negative number.