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Governments want you to save for retirement, so they offer tax-advantaged accounts, wrappers that shelter your investments from taxes. In the US the big ones are the 401(k), offered through employers, and the IRA, which you open yourself; most other countries have equivalents (ISAs and pensions in the UK, TFSAs and RRSPs in Canada, superannuation in Australia). The investments inside can be the same index funds from the last lesson; the wrapper just changes the tax treatment.
The key US distinction is traditional versus Roth. Traditional accounts give you a tax break now (pre-tax contributions) and tax the withdrawals in retirement. Roth accounts flip it: you contribute after-tax money, and qualified withdrawals in retirement are completely tax-free. A rough rule of thumb: Roth tends to favor people who expect to be in a higher tax bracket later, which often includes people early in their careers.
One rule towers above all the others: if your employer matches 401(k) contributions, capture the full match before doing anything else. A typical match is an instant, guaranteed 50 to 100 percent return on those dollars, which is the single best deal in all of personal finance. Contribution limits and income rules change year to year, so verify the current numbers on official sources when you set up your accounts.