The mortgage on your house in Winnipeg is five years old. It required monthly payments of $$1,450,$ had an original term of $30$ years, and had an interest rate of $8\%($APR with semi$-$annual compounding$).$ In the intervening five years, interest rates have fallen, housing prices in the United States have fallen, and you have decided to retire to Florida. You have decided to sell your house in Winnipeg and use your equity for the down payment on a condo in Florida. You will roll over the outstanding balance of your old mortgage into a new mortgage in Florida. The new mortgage has a $30-$year term, requires monthly payments, and has an interest rate of $5\mathrm{.}625\%($APR with monthly compounding which is typical for U S mortgages$).($Note: Be careful not to round any intermediate steps less than six decimal places.$)$

a$.$ What monthly repayments will be required with the new loan?

b$.$ If you still want to pay off the mortgage in $25$ years, what monthly payment should you make on your new mortgage?

c$.$ Suppose you are willing to continue making monthly payments of $$1,450.$ How long will it take you to pay off the new mortgage?

d$.$ Suppose you are willing to continue making monthly payments of $$1,450$ and want to pay off the mortgage in $25$ years. How much additional cash can you borrow today as part of the new financing?

$($Note: Be careful not to round any intermediate steps less than six decimal places.$)$

a$.$ What monthly repayments will be required with the new loan?

The monthly repayments with the new loan will be $$1093\mathrm{.}76.($Round to two decimal places$)$

b$.$ If you still want to pay off the mortgage in $25$ years, what monthly payment should you make on your new mortgage?

The monthly repayments will be $$.($Round to two decimal places.$)$