You are working with a client who would like to build an $80-$unit apartment complex that includes $50$ one$-$bedroom apartments and $30$ two$-$bedroom apartments. The client has $\backslash (\backslash$$ $1\backslash$mathrm$\{$MM$\}\backslash )$ of his own money but would need to secure a loan from a bank for the remainder of the funds needed. What would the client need to charge as monthly rent for both one$-$bedroom and two$-$bedroom apartments to have a return of $\backslash (10\backslash \%\backslash )($per year, compounded annually$)$ after $10$ years?

CONSTRUCTION COSTS:

$-$ Land purchase:

$\backslash$$$1\mathrm{.}1$MM

$-$ Site preparation:

$\backslash (\backslash$$ $0\mathrm{.}5\backslash$mathrm$\{$MM$\}\backslash )$

$-$ Utilities:

$\backslash (\backslash$$ $0\mathrm{.}3\backslash$mathrm$\{$MM$\}\backslash )$

$-$ Site preparation, landscaping, parking lots, common areas, etc.: $\backslash (\backslash$$ $0\mathrm{.}4\backslash$mathrm$\{$MM$\}\backslash )$

$-$ Construction costs: $\backslash (\backslash$$ $200/\backslash )$ square foot $($Each $1-$bedrm $-900$ sq$.$ft$./2-$bedrm $\backslash (-1400\backslash$mathrm$\{$sq$\}.\backslash$mathrm$\{$ft$\}\backslash ).)$

$-$ Engineering costs: $\backslash (10\backslash \%\backslash )$ of the total construction cost $($less the land purchase$)$

FINANCING COSTS:

$-$ Bank loan:

Remainder of the construction costs at $\backslash (6\backslash \%\backslash )$

$-$ Community incentive: $\backslash (\backslash$$ $250\backslash$mathrm$\{$~K$\}\backslash )$

ANNUAL COSTS:

$-$ Operational $\backslash$& Maintenance costs: $\backslash (10\backslash \%\backslash )$ of initial capitalized costs $($less the land purchase$)$

$-$ Property taxes: $\backslash (3\backslash \%\backslash )$ of book value

$-$ Depreciation $($straight line$)$ over $30$ years.

$-$ Occupancy rate of $\backslash (50\backslash \%\backslash )$ first year and $\backslash (80\backslash \%\backslash )$ thereafter $($both types of units$)$

FINAL RESULT:

$-$ Market value at the end of $10$ years: $\backslash (80\backslash \%\backslash )$ of initial cost