Yes there is a form to file to make payments. I just happen to have my 1040 here so I could make copies and send it in today. On the 1040 line #67 it says,
"Amount paid with requenst for extension to file (see page 56)."
Now on page 56 of the instructions it says,
"file Form 4868 to get an automatic extension of time to file Form 1040..."
Just download
Form 4868 and follow its instructions. Then you can file Form 1040 later than April 15th. I'd suggest you pay as much as you can now (and you seem to have most of it already) to minimize interest. The interest rate is 0.5% per month (about 6.2% per year) if you properly file Form 4868. This is a very easy form to fill out - basically your name, address, and how much you want to borrow. Very simple.
You asked about under reporting. Line 74 on Form 1040 says,
"Estimated tax penalty (see page 57)."
Lets look on page 57,
"You may owe this penalty if" you owe "at least $1,000 and it is more than 10% of the tax shown on your return".
You owe more than $1000 which meets the first criteria. Now if your total tax is less than $35,000 you owe a penalty because you meet that second criteria - you didn't pay enough taxes throughout the year. Our tax system is a pay as you go system. You are required by law to pay a minimum of 90% of your tax you owe each and every paycheck (or stock sale or whatever earned you money). If your total tax is less than $35,000 then you didn't pay that minimum of 90%. Thus you likely owe a penalty. File
Form 2210 to find out how much the penalty is. Warning, Form 2210 is complicated and you can ask the IRS to fill it out for you and send you a bill for your penalty.
By the way, this is all in your instruction booklet that the IRS mailed you. I don't use tax software since the taxes I owe are pretty straightforward and the instructions are very helpful telling you step by step what to do. But even with using tax software, you can still look up the instructions quickly and easilly by hand.
