Your have just sold your house for $ $900,000$ in cash. Your mortgage was originally a$30-$year mortgage with monthly payments and an initial balance of $ $700,000.$ The mortgage is currently exactly $18\mathrm{.}50$ years$$ old, and you have just made a payment. If the interest rate on the mortgage is $6\mathrm{.}25\%($APR$),$ how much cash will you have from the sale once you pay off the$$ mortgage? $($Ignore any real estate transaction$$ costs.$)$

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Part $1$

The discount rate is

$$

enter your response here$\%$ per month.$($Round to five decimal$$ places.$)$

Part $2$

The monthly mortgage payment is $$$

$$

enter your response here. $($Round to the nearest$$ cent.$)$

Part $3$

The remaining balance is $$$

$$

enter your response here. $($Round to the nearest$$ dollar.$)$

Part $4$

The cash that remains after payoff of the mortgage is $$$

$$

enter your response here. $($Round to the nearest$$ dolla$)$