Projections using an actuarial model of the U.S. social security system suggest that diverting two percentage points of the current social security tax into individual accounts is likely to worsen the program's long-range deficit. The conditions necessary to avoid this result include: (1) equity returns in the future at least equal to those of the past, (2) investment of at least half of the account balances in equities, (3) centralized administration and passive investment policies to assure low administrative costs, and (4) recapturing (i.e., taxing away) at least 75 percent of the account balances at retirement. Even if a plan can be introduced that avoids an increase in the long-range deficit, financing the transition costs would require additional government borrowing that peaks at over $6 trillion in today's prices, or equivalent reductions in other government spending. These results suggest that no matter how attractive the idea may be in theory, diverting part of the current payroll tax to individual accounts is not likely to be a very effective solution to today's Social Security financing problem.