$($Q$)$ You can afford to pay up to $$4000$ in mortgage payments every month for housing

and have $$80,000$ in savings $($you don't anticipate and increase in income$/$savings$).$

Which of the following mortgages would allow you to buy the most expensive property?

A $30$ year fully amortizing FRM with $8\mathrm{.}2\%$ contract interest rate and $85$ LTV $[$a$]$

A $25$ year FRM with $6\mathrm{.}5\%$ contract interest rate and $\mathrm{.}9$ LTV$.[$b$]$

A $30$ year FRM with $8\mathrm{.}2\%$ contract interest rate, $\mathrm{.}9$ LTV and a balloon payment of

$$80,000$ at the end of the $5$ th year $[$c$]$

A $30$ year mortgage with an interest only period of $5$ years at a fixed contract rate

$8\%$ and $0\mathrm{.}95$ LTV $.[$d$]$Please show all calculations and steps