You just took out a $$90000$ mortgage for piece of lake$-$front land in northern Alberta. You negotiated with your bank for a $9\mathrm{.}5\%$ nominal interest rate $($compounded monthly$)$ and

a $20-$year amortization period $($the duration over which the loan is calculated to be repaid$).$ Please use the factor formula to solve the questions below:

$($a$)$ Calculate your monthly payments.

Monthly payments $=$$

$($b$)$ A short time later, you're interested in refinancing your mortgage. How much do you still owe after three years?

$=$$

$($keep $2$ decimal places$)$