Suppose that $15$ years ago you bought a home for $$500,000,$ paying $20\%$ as a down payment, and financing the rest at $5\%$ interest for $30$ years. How much money did you pay as your down payment?

$[2$ points$]$ How much money was your existing mortgage $($loan$)$ for?

$[2$ points$]$ What is your current monthly payment on your existing mortgage? Note: Carry at least $4$ decimal places during calculations, but round your final answer to the nearest cent.

$[2$ points$]$ How much total interest will you pay over the life of the existing loan?

$[2$ points$]$ This year $(15$ years after you first took out the loan$),$ you check your loan balance. Only part of your payments have been going to pay down the loan; the rest has been going towards interest. You see that you still have $$271,536$ left to pay on your loan. Your house is now valued at $$650,000.$ How much of the original loan have you paid off? $($i$.$e$,$ how much have you reduced the loan balance by$?$

$[2$ points$]$ How much money have you paid to the loan company so far $($over the last $15$ years$)?$

$[2$ points$]$ How much interest have you paid so far $($over the last $15$ years$)?$

$[2$ points$]$ How much equity do you have in your home $($equity is value minus remaining debt$)?$

$[2$ points$]$ Since interest rates have dropped, you consider refinancing your mortgage at a lower $3\%$ rate. If you took out a new $30$ year mortgage at$3\%$ for your remaining loan balance, what would your new monthly payments be$?$

$[2$ points$]$ How much interest will you pay over the life of the new loan?

$[2$ points$]$ Notice that if you refinance, you are going to be making payments on your home for another $30$ years. In addition to the $15$ years you$$ve already been paying, that$$s $45$ years total. How much will you save each month because of the lower monthly payment?

$[2$ points$]$ How much total interest will you be paying $($consider the interest you paid over the first $15$ years of your original loan as well as interest on your refinanced loan$)?$

$[1$ point$]$ Now the non$-$computational question: Does it make sense to refinance? $($There isn$$t a correct answer to this question. Just give your opinion and your reason.$)$

$3-13$ please