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1) Was I suppose to pay taxes on the capital gains as they were realized.

Yup, you pay taxes as income are realized. U.S. tax system is a "pay-as-you-go".

I had assumed that I could wait until the end of the year, since I could have losses that would offset the gains.

Nope, tax are paid when realized. Tax are paid through employer withholding and "quarterly" estimated tax payment. See below for some details or see IRS Publication 505 Withholding and Estimated Tax for full detail.

If I pay 105% of the taxes that I paid in 1998, then have I found a Safe Harbor?

The 105% is the amount of withheld tax, not estimated tax payment, which are not included in this safe harbor calculation. If your company is willing, ask them to withhold additional amount to reach the safe harbor. If the withholding doesn't reach the safe harbor, then you're in trouble.

In the case that your withholding doesn't reach the safe harbor, you are required to make estimated tax payment for each periods (first period is from Jan 1 to Mar 31 w/ due date of Apr 15; 2nd period Apr 1 - May 31 : Jun 15; 3rd period Jun 1 - Aug 31 : Sep 15; 4th period Oct 1 - Dec 31 : Jan 15).

There are 4 ways to make estimated tax payment:
Option 1) make one lump-sum estimated tax payment on Apr 15 -- unless you're psychic and know exactly how much your capital gain for the whole year is, you won't be able to use this option.
Option 2) make equal installment payment -- again, unless you're psychic, you won't be able to use this option.
Option 3) make uneven estimated tax payment per period. To do this, you calculate all your income for the period only, minus capital loses, deduction, credit, etc, and pay tax based on that amount. Note that this is a per period--if you have capital loss later, it doesn't factor in.
Option 4) make uneven estimated tax payment through annualized income. To do this, your income is calculated from the beginning of the year to the current period. This method is used when most of the gain is made later in the year. Since most of your gains is in the 3rd period, you should use this method.

The safe harbor is per period, so by failing to make estimated tax payment in the first 3 periods, you will owe penalty unless . . .

You beg/plead/entice your employer to withhold more tax to reach the 105% of 1998 tax liability. You can do this by filing a new W4 with 0 allowance and by putting in an additional withholding amount. Some employer may withhold your whole check--most won't. So give payroll some early Christmas gifts. And if you don't have enough income to withhold the necessary amount, ask your employer to pre-pay you for the next year. Most won't, but you got nothing to lose.

If that doesn't happen, then make an estimated tax payment on Jan 18, 2000. You are still penalized for the first 3 periods, but at least you won't be penalized for the last period.

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