A $25-$year, $$470,000$ mortgage at $4\mathrm{.}20\%$ compounded quarterly is repaid with monthly payments.

a$.$ What is the size of the monthly payments?

$$0\mathrm{.}00$

Round to the nearest cent.

b$.$ Find the balance of the mortgage at the end of $8$ years?

$$0\mathrm{.}00$

Round to the nearest cent.

c$.$ By how much did the amortization period shorten by if the monthly payments are increased by $$150$ at the end of year eight?

$0$

years

$0$

months

Express the answer in years and months, rounded to the next payment period.