Determine the outstanding principal of the given mortgage. $($Assume monthly interest payments and compounding periods. Round your answer to the nearest cent.$)$

a $$100,000,36-$year, $4\mathrm{.}6\%$ mortgage after $10$ years

a$)$ First, what is the payment for the mortgage? $--$ What formula do you use to find this value?

SI $=$ P$(1+$ rt$)$

CI $=$ P$(1+$ r$/$m$)$mt

FV $=$

PMT$((1+$r$/$m$)$mt $-1)$

$($r$/$m$)$

PV $=$

PMT$(1-(1+$ r$/$m$)-$mt$)$

$($r$/$m$)$

UB $=$

PMT$(1-(1+$ r$/$m$)-($tm$-$pm$))$

$($r$/$m$)$

b$)$ Now, that we have the payment. How do we find amount left in the mortgage after $10$ years? $--$ What formula do you use to find this value?

SI $=$ P$(1+$ rt$)$

CI $=$ P$(1+$ r$/$m$)$mt

FV $=$

PMT$((1+$r$/$m$)$mt $-1)$

$($r$/$m$)$

PV $=$

PMT$(1-(1+$ r$/$m$)-$mt$)$

$($r$/$m$)$

UB $=$

PMT$(1-(1+$ r$/$m$)-($tm$-$pm$))$

$($r$/$m$)$