Suppose you want to buy a house for $$420,000$ and you have $$40,000$ in savings you can use as a down payment.

The rest you finance with a $5-$year mortgage $($monthly payments$)$ with a quoted interest rate of $5\mathrm{.}34\%($APR$)\mathrm{.}1$

Assume that this mortgage is amortized over $25$ years.

a$)$ What are the monthly payments over the $5-$year term of the mortgage?

b$)$ How much do you still owe three years after you took out this mortgage $($i$.$e$.,$ immediately after you made the

$36$th monthly payment$)?$

c$)$ What is the principal portion of the $37$th mortgage payment?

d$)$ What would be the bi$-$weekly payments $($you would make payments once every two weeks$)$ if you switched to

bi$-$weekly payments right after you made the $36$th monthly payment. Assume there is no penalty for switching

and that the effective interest rate remains the same. Also assume that you would make bi$-$weekly payments for

the remainder of the term, i$.$e$.,22$ years, and that a year has exactly $52$ weeks.

e$)$ Suppose your bank offers you a car loan with a monthly compounded APR of $5\mathrm{.}34\%.$ Which of the two loans is

$$cheaper:$$ the mortgage or the car loan? Or are you paying the same effective interest rate on both?