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.

$1.$ What was the size of each monthly payment?

$2.$ What is the cost of the mortgage for the first $5$ years?

$3.$ In November $2020,$ they decided to refinance their mortgage since rates were down by

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?

Note: Please provide step to step explanation by using formulas. I don't want my solution by the help of Excel or table charts....