Is Zakat obligatory on a sum of money that reaches the Nisab at the end of the year, provided that it has been invested in a project, with an additional debt added to the sum to complete the project?

The invested amount is subject to Zakat if its principal has completed a [lunar] year and reached the minimum threshold (nisab). Any debt you owe is deducted from your wealth. Whatever remains thereafter is subject to Zakat if it reaches the nisab and a year has passed over it.