David purchased a property for $$2$ million and arranged a mortgage with DBS bank to borrow $80\%$ of the property value. The current mortgage rate is $3\mathrm{.}5\%$ p$.$a$.$ David intended to repay his mortgage over $20$ years. The mortgage repayment is made at the beginning of every month.

Required:

$($a$)$ Compute the principal and interest repayments separately, which David has paid in total for first $3$ months.

$(6$ marks$)$

$($b$)$ David expects the interest rate would increase by $50$ basis points $(0\mathrm{.}5\%)$ if he borrows one month later, but he still wants to pay a same monthly repayment for his mortgage, what advice could you give to David?

$(4$ marks$)$