A $30-$year mortgage for $$175,000$ is issued at a $6\%$ nominal interest rate.

$($a$)$ What is the monthly payment?

$($b$)$ How long does it take to pay off the mortgage, if $$1250$ per month is paid?

$($c$)$ How long does it take to pay off the mortgage, if double payments are made?

the answer at the back of the book shows

a$)$ payment $$1049\mathrm{.}21,$ b$)241\mathrm{.}4$ months,c$)108\mathrm{.}2$ months