Question $7.(35$pts$)$

A couple takes out a $$500,000$ mortgage from their favorite bank. They plan on paying it off over $25$ years through bi$-$weekly payments. They opt for a fixed$-$rate, $5-$year term mortgage that carries an interest rate of $6\frac{\%}{?}$ year compounded semi$-$annually. At the end of this term, the mortgnge mill nood to be renewed and the rate may change.

$($a$)$ Calculate the regular payment $($under the usual assumption that the $6\%$ rate continues for the entire $25$ ycars$).$

$($b$)$ Show the first two rows of the amortization schedule.

$($C$)$ what is the oustanding balance after....

i$)3$ years

ii$)5$ years?

d$)$ During the initial $5$ year term, there is a penalty of $6$ months' payments on any proncipal repaid early. After $3$ years, the bank's interest rate on $2$ year mortgages falls to $4\mathrm{.}75\%/$year compounded semi$-$annually. Calculate the new bi$-$ weekly payment if the loan is refinanced and set up to have the same outstanding balance at the end of the initial $5-$ year term. Would it pay to refinance?