Estimate penalty and interest on an overdue amount using your applicable rates. The model uses a 365-day year and 12 equal months; choose prorated or started penalty periods. It does not calculate an official tax bill or include changing rates, payments, interest on penalties or statutory exceptions.
Penalty and Interest Formula
Penalty = A × (P ÷ 100) × n
Interest (simple) = A × (r ÷ 100) × t
Interest (compound) = A × [(1 + (r ÷ 100) ÷ m) ^ (m × t) − 1]
Total Owed = A + Penalty + Interest
The variables are:
A is the overdue amount (the unpaid balance the penalty and interest apply to).
P is the penalty rate, expressed as a percent. It can apply per month, per day, or as a single one-time charge.
n is the number of penalty periods late (months or days) that match the penalty basis. For a one-time flat penalty, n is not used.
r is the annual interest rate as a percent.
t is the time late expressed in years.
m is the number of compounding periods per year (365 for daily, 12 for monthly) and is only used for compound interest.
The penalty is a charge for paying late, usually set as a fixed percent of the unpaid amount per month or per day. The interest is a separate charge that accrues on the unpaid amount over time. You add both to the original amount to get the total owed. When a maximum penalty cap is set, the penalty stops growing once it reaches that percent of the amount.
Typical Penalty and Interest Rates
The IRS entries summarize general rules, with exceptions; see the IRS failure-to-pay rules, failure-to-file rules and interest rules. This fixed-rate model is not an IRS assessment. Use the rates and period rules from your bill, contract or authority.
| Source | Penalty | Interest |
|---|---|---|
| IRS failure to pay | Generally 0.5% per month or part of a month, max 25%; exceptions apply | Federal short term rate plus 3%, compounded daily |
| IRS failure to file | Generally 5% per month or part of a month, max 25%; reduced when both penalties apply | Same daily interest as above |
| Typical commercial invoice | Use the applicable contract and law | Set by contract or state law |
| Many state tax agencies | Use the applicable state rules | Use the applicable state rate |
Example Problems
Example 1. You owe an overdue amount of $5,000 that is 6 months late. The penalty is 0.5% per month and the annual interest rate is 8% using simple interest.
The penalty is 5000 × (0.5 ÷ 100) × 6 = $150.00. With 12 equal model months per year, interest is 5000 × (8 ÷ 100) × 0.5 = $200.00. The estimated total is 5000 + 150 + 200 = $5,350.00.
Example 2. You owe $2,000 that is 30 days late. The agreement charges a one-time flat penalty of 10% and no interest.
The penalty is 2000 × (10 ÷ 100) = $200.00. With no interest, the total owed is 2000 + 200 = $2,200.00.
Frequently Asked Questions
What is the difference between a penalty and interest?
A penalty is a flat charge for paying late, usually a set percent of the unpaid amount applied once or per period. Interest is a separate, ongoing charge that grows the longer the amount stays unpaid. Most late bills include both, so you add them together to find the full total owed.
Should I use simple or compound interest?
Use simple interest when the rate is applied only to the original unpaid amount. Use compound interest when interest is added to the balance and then earns more interest, which is how many tax agencies calculate it with daily compounding. Choose the interest method and, for compound interest, daily or monthly compounding.
What does the maximum penalty cap do?
The cap limits how large the penalty can grow. For example, many tax penalties stop at 25% of the unpaid amount no matter how late the payment is. If you enter a cap, the penalty is held at that percent of the amount once it is reached, while interest can keep accruing.
