$($Please show work using Excel$)$ A real estate company buys a $$420,000$ property with $10\%$ down and a $12$ year loan with an annual rate of $5\mathrm{.}2\%.$

What are the monthly payments?

After purchasing the property, the company determines that the value will grow at a monthly rate of $0\mathrm{.}10\%$ and can be rented out for $$2,100$ a month with the rent starting at the first month.

How many months will it take the equity to equal $50\%$ of the value of the property?

In the second year, months $13$ thru $24,$ the company pays an additional $$500$ a month on the mortgage.

The company sells the property after five years with the expectation that it will have an annual return of $15\%$ a year.

Determine the actual annual return that the company achieves over the five years? What happened?

What percent of the total equity at month $60$ was due to the growth rate? What percent was due to the paying down of the principal?

Create a data table with the annual return as the output. The column input is the additional amount paid on the mortgage, start with $$0$ and go to $$500$ in increments of $$100.$ Do the numbers make sense? Explain.

Before you do this last part create a new tab so that the changes you make don't affect your answers to the questions above.

After the additional $$500$ month is added to the mortgage, from month $13$ to month $24,$ what would the monthly rent have to be in order to reach an annual return of $15\%?$