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? Problem $1)$ a$)$ What are the monthly payments over the $5-$year term of the mortgage?

Question $1$Select one:

a$.$$$2,284$

b$.$$$1,267$

c$.$$$2,269$

d$.$$$2,297$

e$.$$$20,292$

f$.$$$2,525$

g$.$$$16,085$

h$.$$$27,888$

Problem $1)$ 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$)?$

Question $2$Select one:

a$.$$$334,400$

b$.$$$355,973$

c$.$$$356,194$

d$.$$$356,382$

e$.$$$380,000$

f$.$$$393,688$

g$.$$$336,572$

h$.$$$355,477$

Problem $1)$ c$)$ What is the principal portion of the $37$th mortgage payment?

Question $3$Select one:

a$.$$$1,568$

b$.$$$717$

c$.$$$812$

d$.$$$722$

e$.$$$711$

f$.$$$948$

g$.$$$856$

h$.$$$946$

Problem $1)$ 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?

Question $4$Select one:

a$.$$$1,643$

b$.$$$1,164$

c$.$$$9,510$

d$.$$$544$

e$.$$$1,053$

f$.$$$1,706$

g$.$$$1,059$

h$.$$$821$

Problem $1)$ e$)$ Which of the two loans is cheaper: the mortgage or the car loan?

Question $5$Select one:

a$.$ The car loan is "cheaper" with an EAR of $5\mathrm{.}34\%$

b$.$The EAR of the car loan is less than the EAR of the mortgage

c$.$The effective monthly rate of the car loan is $0\mathrm{.}445\%$ and is less than the effective monthly rate of the mortgage

d$.$The mortgage has an EAR of $5\mathrm{.}411\%$ and is "cheaper" than the car loan, which has an EAR of $5\mathrm{.}473\%$