Mr$.$ Smith is purchasing a $$130000$ house. The down payment is $20\%$ of the price of the house. He is given the choice of two mortgages:

a$)$ a $30-$year mortgage at a rate of $10\%.$

Find

$($i$)$ the monthly payment: $

$($ii$)$ the total amount of interest paid: $

b$)$ a $15-$year mortgage at a rate of $10\%.$

Find

$($i$)$ The monthly payment: $

$($ii$)$ the total amount of interest paid: $