Mohsen Manouchehri plans to purchase a $$230,000$ home with a down payment of $20\%$ and

financing the rest. He has the choice of two loans: a $20-$year loan with an interest rate of $3\mathrm{.}3\%$ or a

$30-$year loan with an interest rate of $2\mathrm{.}9\%.$

A$.$ Set up the amortization payment formula with the proper values for the variables for each of

the loans:

$=$

$$

$[$

$1(1+)$

$$

$$

$]$

B$.$ Calculate each loan$$s monthly payment.

C$.$ How much will he owe after making payments for $8$ years? Examine the remaining balance

formulas below for each loan and explain what the numbers that have replaced the variables in

the formulas represent.

For the $20$ year loan: $=1048\mathrm{.}31[$

$1(1+$

$\mathrm{.}033$

$12$

$)$

$(24096)$

$\mathrm{.}033$

$12]$

For the $30$ year loan: $=765\mathrm{.}86[$

$1(1+$

$\mathrm{.}029$

$12$

$)$

$(36096)$

$\mathrm{.}029$

$12]$

D$.$ How much in total interest will he pay over the term of each loan? Show all of your

calculations. What assumptions did you make when doing these calculations?