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

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

Enter your answer as a positive number. Round to the nearest cent.

How much interest will be in your first payment?

Enter your answer as a positive number. Round to the nearest cent.

How much principal will be in your first payment?

Enter your answer as a positive number. Round to the nearest cent.

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

Enter your answer as a positive number. Round to the nearest cent.

How much interest will be paid in the first $50$ payments?

Enter your answer as a positive number. Round to the nearest cent.

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

Enter your answer as a positive number. Round to the nearest cent.

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$?$

Enter your answer as a positive number. Round to the nearest cent.

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 the refinancing opportunity?

Round to the nearest cent.

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 than if you had paid closing costs up front$),$ what would the NPV of the refinancing opportunity be$?$

Round to the nearest cent.

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 house for the discount point to be worth the cost?

Margin of error is set to $+/-1$ month of the exact answer.