Mortgage amount: $$500,000$

Rate: $7\%$ APR

Term: $360$ Months

$1)$ How much of the first month's payment is paydown of the principal amount?

$2)$ After $5$ years, what is the mortgage balance outstanding?

$3)$ If in $5$ years, you refinance at $6\%$ APR for a new $25$ year monthly mortgage loan, how much interest savings over the life do you save?

$4)$ If in $5$ years you refinance as above at $5\mathrm{.}25\%,$ what would be the net present value of refinancing if the refinance fee is $$4,000$

$5)$ If you were to make the decision to refinance as above in $5$ years, how long must you live in the house to recover the refinance fee of $$4,000?6)$ If you were to pay off the new $25$ year monthly mortgage at $5\mathrm{.}25\%$ over $15$ years...how much interest would you save?