It sounds like you are referring to Social Security retirement benefits, not SSI benefits. SSI is a welfare program for the disabled and elderly. Social Security retirement benefits, on the other hand, are earned by paying into the Social Security system during your working years. If you are eligible for Social Security retirement benefits, you can begin to collect benefits at age 62. The amount of your benefit will be less than it would be if you waited until your "full retirement age" -- probably 66. In addition, if you collect retirement benefits at 62 and you continue to work, your retirement benefit will be reduced by $1 for every $2 that you earn in excess of $15,200 per year. If you wait until age 66 (or later) to receive your retirement benefits, there will be no deduction for earned income. The longer you delay receiving benefits, the higher your benefit amount will be. You can see how this works for your particular situation by going to the Social Security website and using their "retirement calculator." www.ssa.gov.
Supplemental Security Income (SSI) is a means-tested welfare program for the blind, disabled, and persons age 65 and older of low income and little in assets. It is often confused with Social Security, which is an insurance program that provides benefits wage-earners who are disabled or over age 62 and their dependents and survivors. There is so much overlap in the types of beneficiaries, disability medical requirements, and other details that the two programs are widely confused, even by attorneys. A 62-year-old could be an SSI beneficiary if the disability standards have been met.
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I'll add my 2 cents to Paula's answer: generally, when you hear people talking about receiving Social Security at age 62 or 65, they are referring to SS retirement. Most people who have worked and paid SS taxes are eligible to retire at 65 or 66, whatever their full retirement age is. When someone retire at 62, that is the so called "early retirement" where you have to pay a penalty for drawing your retirement benefits earlier. There certainly is a lot of confusion related to SS benefits, and eligibility for each type of benefit depends on the facts of each case.
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