$1.)$Assume that Larry borrows $$500,000$ in a five$-$year debt contract, and that he is scheduled to pay back $$600,000$ when the debt matures in five years. Assuming this is a simple loan with no coupon payment at the meantime, what$$s the annual interest rate assuming that the rate compounds annually?

$3\mathrm{.}71\%$

$4\mathrm{.}00\%$

$4\mathrm{.}51\%$

$3\mathrm{.}56\%$

$2.)$Tommy borrows $$450,000$ to finance his recent purchase of a dream home in the form of a fixed$-$payment$/$fully amortized loan $($i$.$e$.$ in the form of a fully amortized mortgage$).$ Assuming that $1)$ this is a standard $30-$year mortgage contract, $2)$ the annual interest rate is $7\mathrm{.}2\%,$ and $3)$ the interest rate will compound monthly, what will be the amount of Tommy$$s mortgage payment?

$$2,940\mathrm{.}92$

$$3,156\mathrm{.}46$

$$3,054\mathrm{.}55$

$$3,124\mathrm{.}75$