In a "honey moon" loan the borrower borrows $$200$K and is charged interest rate $2\%($per annum$)$ for the first $3$ years and then $6\%($per annum$)$ for the rest of the loan.

Payments are made monthly at the end of the month. The loan is an interest only loan and will end after $20$ years.

$($i$)$ Calculate the payment per month that the borrower makes in the first $3$ years. $($ii$)$ Calculate the payment per month for the rest of the loan.

$5.$ What is the effective overall interest rate on average over the whole loan.