Hassan and Dana had bought a property valued at $$1,225,000$ for $20\%$ down and a mortgage amortized over $25$ years on March $1,2018.$ They made equal end$-$of$-$month payments towards their mortgage. Interest on the mortgage was $3\mathrm{.}29\%$ compounded semi$-$annually and the mortgage was renewable after five years.

$9.$ What was the size of each monthly payment?

$10.$ Whatisthecostofthemortgageforthefirst$5$years?

$11.$ InNovember$2020,$theydecidedtorefinancetheirmortgagesinceratesweredownby quite a lot. Suppose the new rate they qualified for was $1\mathrm{.}74\%$ compounded semi$-$annually and they could borrow enough to cover their remaining mortgage balance. The new mortgage is amortized over $25$ years, but they also need to pay a penalty for breaking the old mortgage early.

If the penalty is the interest differential over the remaining term of the old mortgage $($under the old and the new rates$),$ and if the penalty is also added to the new mortgage, what is the size of their new monthly payment?