Q$.1$ Fixed vs$.$ Floating Rate $(50$ marks$)$

An ongoing debate regarding financial decisions is whether to lock in our mortgages at a $$fixed$$ or $$floating$$ rate. Consider the following scenario.

You plan to apply for a mortgage of $$700,000$ to buy your dream house. Your bank gives you the following two choices:

A$)$ Enter into a fixed$-$rate mortgage at a quoted rate of $4\mathrm{.}09\%$ compounded monthly for a five$-$year term.

B$)$ Enter into a variable mortgage at a quoted rate of $4\mathrm{.}45\%$ compounded monthly for a five$-$year term.$$

Assume that the payments will be made monthly $($at the end of the month$)$ and that the mortgage will be set up initially with an amortization period of $30$ years.$$

$1.$ Determine the required monthly payments under each option. $(10$ marks$)$

$2.$ Assume the floating rate doesn$$t change; what option would you choose? Determine the $$non$-$discounted$$ value of total savings over the five$-$year term under your choice. $(5$ marks$)$

$3.$ Assume that the floating rate changes $$once$$ during the five$-$year term, and assume that this happens at the end of the second year. Determine how much the floating rate would have to decrease for you to be $$indifferent$$ between two options in economic terms. $(25$ marks$)($Hint: you can reduce your monthly payment under the floating rate option to be $$indifferent$$ between the two options$).$

$4.$ Assume the floating rate decreases $$once$$ by $1\%$ during the five$-$year term, which happens at the end of year $1,$ calculate the principal outstanding for both options at the end of year $5.$ Assume that monthly payments under both the options remain same as calculated in part $1.(10$ marks$)$