Suppose you purchased a house $3$ years ago and took out a mortgage for $$200,000$ with a $7\mathrm{.}5\%$ interest rate. The mortgage is a $30$ year mortgage with monthly payments. Today you can refinance the loan at a $6\mathrm{.}5\%$ interest rate for a fee of $$7,500.$ Assume that you would only refinance enough to repay the old loan and the cost of refinancing.

$\backslash$table$[[,$Annual Rate,Life $($In Years$),$Loan Amount,$\backslash$table$[[$Monthly$],[$Payments$]],$Periods Paid,Cost,$],[$Initial Loan,$7\mathrm{.}50\%,30,$$$200,000\mathrm{.}00,$$$1,398\mathrm{.}43,36,$$$,],[$Refinancing$,6\mathrm{.}50\%,30,$$$194,028\mathrm{.}50,$$$1,226\mathrm{.}39,0,$$$,7,500\mathrm{.}00$