Increasing the down payment on a mortgage reduces both the size of the monthly payments and the total interest paid. Calculate $($a$)$ the reduction in the monthly payment by increasing the down payment by the amount specified, and $($b$)$ the amount saved on interest over the life of the loan. Assume the mortgage is for $30$ years and use the amortization table to find the monthly payments.

$\backslash$table$[[$Amount of Loan,Interest Rate,Down Payment,$\backslash$table$[[$Increase in$],[$Down payment$]]],[$$$160,000,12\%,$$$31,000,$$$5,000$