IRS compound interest and penalty help

[itchylipid]

problem:

Rental income was not claimed for 180 months. Figuring the income at $1000 per month, I would like to calculate the interest and penalties.

According to the IRS, this is 5.5% on the accrued total unpaid taxes due, calculated monthly (ouch).

There was a down payment of $30,000 from another party which should have been reported as income as well. The tax bracket is about %40. So %40 of $30,000 = 12,000.

So, the first month the interest and penalties would be due on approx. $12,000 in taxes due: .055 x $12,000 x = $660 interest and penalties owed.

the second month it would be $660 + .055 x $12,400 (12,000 plus %40 of the mortgage of $1,000 = $400) = $660 + $682 = $1342.

the third month is $1342 + .055 x $12,800 = $1342 + $704 = $2046 and so on.

Is there a convenient formulaic way to express this? Other wise it's a long way to 180 months

A reasonable approximation would be welcome too.

 

[Denis]

> So, the first month the interest and penalties would be due on approx. $12,000 in taxes due:
> .055 x $12,000 x = $660 interest and penalties owed.

That should be 12000 * .055 / 12 = 55; the way you're doing it means 5.5 * 12 = 66% per year:
even the IRS is not that cruel!

> the second month it would be $660 + .055 x $12,400 (12,000 plus %40 of the mortgage of
> $1,000 = $400) = $660 + $682 = $1342.

NO; not that simple.
2nd month on 12000 + 400 + 55 = 12455 * .055 / 12 = 57.0854...
The 1st month's interest of 55 becomes part of it; that's the meaning of:
"this is 5.5% on the accrued total unpaid taxes due, calculated monthly (ouch)."

The easiest way to handle this is:
pretend it's a savings account in which you deposit $12,000;
then pretend that $400 is deposited monthly for 180 months, beginning a month later;
then calculate the future value of 12000 over 180 months, using .055/12 as interest rate monthly;
and calculate the future value if 180 monthly deposits of 400 (interest as above);
add the two results and that's your solution.

There are formulas for this; if you're unaware of those, well...well... ask your teacher!! :shock: