Yes - you will be charges interest and penalties based on the amount you pay late - after Apr 15.
It is very unlikely that the IRS will abate interest charges, but may abate penalties.
If you owe tax and don't file on time, the total late-filing penalty is usually five percent of the tax owed for each month, or part of a month that your return is late, up to five months.
Generally, interest is charged on any unpaid tax from the due date of the return until the date of payment. The interest rate is determined quarterly and is the federal short-term rate plus 3 percent. Interest is compounded daily. You'll generally have to pay a late payment penalty of one-half of one percent of the tax owed for each month, or part of a month, that the tax remains unpaid from the due date, until the tax is paid in full or the 25% maximum penalty is reached.
You may file form 843 to request the penalties be abated - www.irs.gov/pub/irs-pdf/f843.pdf. Here are instructions - http://www.irs.gov/pub/irs-pdf/i843.pdf
That is a relatively new form - previously the IRS accepted an abate request as a free form letter that may be attached to a tax return or sent separately.
First of all - try the IRS to abate penalties - there is nothing to lose - but in case of success - a part of the problem will be solved.
Let me know if you need any help.