Final answer:
The New Deal program that contributed to social security for unemployment, the disabled, or retirement is the Social Security Act of 1935, which created a federal insurance program funded through a payroll tax.
Step-by-step explanation:
Social Security Act of 1935
The New Deal program that set aside savings through taxes for unemployment, the disabled, or retirement is known as the Social Security Act of 1935. This program played a crucial role in establishing a social safety net during the Great Depression under President Franklin Delano Roosevelt. The act created a pension fund for individuals over the age of sixty-five, supported by a payroll tax on both employees and employers. It also included provisions for unemployment insurance, funded by a tax on employers, as well as programs for people who were blind, deaf, or disabled, and unwed mothers. Although it didn't stimulate immediate economic recovery, Social Security has become the most enduring welfare program from the New Deal era, providing a foundation for financial security in old age, despite the initial exclusion of domestic and agricultural workers.