Suppose you take out a $50-$year $$300,000$ mortgage with an APR of $6\%.$ You make payments for $3$ years $(36$ monthly payments$)$ and then consider

refinancing the original loan. The new loan would have a term of $10$ 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 $$1600.$ Use the information to complete parts $($a$)$ through $($e$)$ below.

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

$$,($Round to the nearest cent as needed.$)$

b$.$ A short calculation shows that the unpaid balance on the original loan after $3$ years is $$296,884\mathrm{.}01,$ which would become the amount of the second

loan. What would the monthly payments be on the second loan?

$$,($Round to the nearest cent as needed.$)$

c$.$ What would be the total amount you would pay if you continued with the original $50-$year loan without refinancing?

$ $($Round to the nearest cent as needed.$)$

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

$$,($Round to the nearest cent as needed.$)$

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

assuming that you can afford the monthly payments.