Question $3$: $[12$ marks total$]$ 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? They wish to keep the original amortization for the loan. $[8$

marks$]$

ii$)$ Show the first two and last two lines of the amortization table of the original

mortgage. $[4$ marks$]$