Rajendran just purchased a new house for Rs$.20,00,000.$ He was able

to make a down payment equal to $20\%$ of the value of the house; the

balance was mortgaged. The rate by the bank is $9\%$ compounded

annually. The mortgage has a $15-$year amortization period $($this means

that payments are calculated assuming it will take $15$ years to pay off the

loan$).$

$($a$)$ What will be the size of the payments by factor formula?

$($b$)$ What will be the balance remaining on the mortgage after $5$ years?