Investment funds around the world are recording accelerated development in the market for capital and represent an important segment of the financial market. In Croatia the market for investment funds is being developed primarily by banks. The investment fund industry is still in a nascent phase of positioning itself on market. Accelerated development of investment funds in Croatia has been helped to a great extent by the reduction of interest rates on deposits, which have been in a constant downward trend for the last two years, by a wide range of various types of funds, and by new ways of thinking about the future financial stability of the country's citizens. This work reviews the open investment funds of Zagrebačka Bank, which are intended for a wide range of investors and which provide professional management of property and a high quality of service. The work analyzes the shortcomings and advantages of an individual fund owned by Zagrebačka Bank and managed by ZB Invest, a company for establishing and managing a UCITS fund. It also examines and presents the knowledge and attitudes of citizens about investments in order to establish their willingness to take on risk by investing in open investment funds. The results of the research demonstrate that citizens have not been completely educated about creating profit by investing in open investment funds and that they are not prepared to take on the risk of investment by themselves.