John has just obtained a variable$-$rate mortgage of $550,000$ to help finance the purchase of his primary residence priced at $700,000.$ The mortgage has a rate j$12=5\%(12$ compounding frequency$),$ amortized over $30$ years with biweekly payment $($hint: how many payments a year?$).$ The term is $5$ years.

$($a$)$ How much is the PMT$?$

$($b$)$ Now at the beginning of the $3$rd year, home price has risen to $800,000.$ John is thinking of using HELOC $($Home Equity Line Of Credit$)$ to obtain cash to pursue other investment opportunities. What is the maximum amount of HELOC he can get? His favorite lender has two conditions for the HELOC amount.

Condition $1$: HELOC amount $<=65\%$ of current home value

Condition $2$: current OSB of the mortgage $+$ HELOC amount $<=80\%$ of current home value