Is zakat due on the capital paid to a computer institute that is still under construction and operation, has not yet achieved a significant return, and what is the zakat's taxable amount and how is it calculated?

There is no zakat due on the capital you both spent on fitting out the shop and purchasing equipment. Zakat is only obligatory on the annual income you earn from the project, provided that each of your shares reaches the zakat threshold (85 grams of gold or 595 grams of silver), and its amount is a quarter of a tenth (2.5%).