The Steins buy a house and take out a $$500,000$ mortgage. The mortgage is amortized over $25$ years with and has a $5-$year term. They make monthly payments at an interest rate of i$^(2)=6\%.$

i$)$ After $4$ years, the interest rates drop to i $^(2)=5\%.$ If a penalty of three months' interest on the outstanding balance is charged to refinance the mortgage, should they refinance the mortgage, why $($show your work$)?$ They wish to keep the original amortization for the loan.

ii$)$ Show the first two and last two lines of the amortization table of the original mortgage. Please draw out the amortization table.