Suppose you take out a $35-$year $$$$300$ comma $000$ mortgage with an APR of $6\%.$ You make payments for $2$ years $(24$ monthly$$ payments$)$ and then consider refinancing the original loan. The new loan would have a term of $15$years$,$ have an APR of $5\mathrm{.}7\%,$ and be in the amount of the unpaid balance on the original loan.$($The amount you borrow on the new loan would be used to pay off the balance on the original$$ loan.$)$ The administrative cost of taking out the second loan would be $$$$2400.$ Use the information to complete parts $($a$)$ through$($e$)$ below.

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Part $1$

a$.$ What are the monthly payments on the original$$ loan?

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enter your response here $($Round to the nearest cent as$$ needed.$)$

Part $2$

b$.$ A short calculation shows that the unpaid balance on the original loan after $2$ years is $$$$294$ comma $644\mathrm{.}82,$ which would become the amount of the second loan. What would the monthly payments be on the second$$ loan?

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enter your response here $($Round to the nearest cent as$$ needed.$)$

Part $3$

c$.$ What would be the total amount you would pay if you continued with the original $35-$year loan without$$ refinancing?

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enter your response here $($Round to the nearest cent as$$ needed.$)$

Part $4$

d$.$ What would be the total amount you would pay with the$$ refinancing?

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enter your response here $($Round to the nearest cent as$$ needed.$)$

Part $5$

e$.$ Compare the two options and decide which one you would choose. What other factors should be considered in making the$$ decision?

The best option would be to

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refinance the loan,

continue paying the original loan,

assuming that you can afford the monthly payments