$1.)$ You want to buy a $$650,000$ house. If you plan to make a $20\%$ down payment, how much will you need to borrow?

Ans: $$520,000$

$2.)$ You plan to get a $15-$year mortgage. If the APR is $4\mathrm{.}8\%,$ what will your monthly payment be$?$

Ans: $$4,058\mathrm{.}16$

$3.)$ How much interest will be in your first payment?

Ans: $$2,080\mathrm{.}00$

$4.)$ How much principal will be in your first payment?

Ans: $$1,978\mathrm{.}16$

$5.)$ What will the loan balance be after $50$ payments have been made?

Ans: $$410,748\mathrm{.}68$

$6.)$ How much interst will be paid in the first $50$ payments?

Ans: $$93,656\mathrm{.}43$

$7.)$ How much principal will be in the $51$st payment?

Ans: $?$

$8.)$ After making $50$ payments, you are considering refinancing the remaining balance with a new $15-$year mortgage because you would be able to borrow at a $3\%$ APR. What would the monthly payment on your new loan be$?$

Ans: $?$

$9.)$ Assume closing costs would equal $6\%$ of the new loan balance, and that these costs would be paid up front. If you feel that you could earn a $9\%$ return on other investment opportunities $($instead of spending money on closing costs to refinance $-$ use I$=9/12$ when calculating NPV$),$ what is the net present value $($NPV$)$ of these refinancing opportunity?

Ans: $?$

$10.)$ If you could roll the closing costs on the new loan into the new loan balance, as opposed to paying the closing costs up front $($resulting in a higher monthly payment on the refinanced loan that if you had paid closing costs up front$),$ what would the NPV of the refinancing opportunity be$?$

Ans: $?$

$11.)$ You want to borrow $$300,000$ for a $30-$year mortgage. You can get a $5\%$ APR with no discount points, or a $4\mathrm{.}8\%$ APR for $1$ discount point $($cost $=1\%$ of loan amount$).$ If you could earn a $9\%$ annual rate of return on other investments $($instead of buying the point $-$ use I$/$Y $=9/12$ to answer this part of the question$),$ how long $($in months$)$ do you need to stay in the hosue for the discount point to be worth the costs?

Ans: $?$

$*$I know $1-6$ are correct, I need help with $7-11.$ Thank you in advance!$*$