Calculate imputed interest on an interest-free or below-market loan from the principal and the AFR, or find a term loan’s PV discount or implied rate.

Simple interest on the gap between the benchmark (e.g. the IRS AFR) and the loan’s rate, at a constant balance.

For US tax purposes this is usually the IRS applicable federal rate (AFR) for the loan’s term and month.

0 for an interest-free loan; otherwise the rate the loan actually charges.

365 days = one year.

Optional settings

Imputed Interest Formula

The simple period estimate below measures forgone interest under constant principal and rates. Term present value and implied compound rate use different formulas; none alone establishes a tax reporting amount.

I = max(0, P × (benchmark% − stated%) / 100 × days / basis)
  • Where I is estimated forgone interest in dollars
  • P is the constant principal in dollars
  • benchmark% and stated% are entered annual rates; no current AFR is supplied
  • days/basis is the selected simple-accrual year fraction

For one maturity payment B at time T, PV = B/(1 + r/m)(mT) and initial discount = max(0, proceeds − PV). Here r is a nominal annual decimal rate and m is compounding periods/year. The effective annual economic rate from one advance P and repayment B is (B/P)(1/T) −1.

Imputed Interest Definition

U.S. below-market loan rules can treat forgone interest or a present-value discount as transfers and interest even when the contract charges less. Demand/gift and other term loans have different rules. This calculator supplies simplified financial estimates; it does not apply statutory exceptions, changing AFRs, payment schedules, OID allocation or tax reporting rules. See IRS Publication550, Below-Market Loans and 26 U.S.C.7872. Section7872 generally specifies semiannual AFR compounding; use the rate and convention applicable to the transaction.

Example Problem

How to calculate imputed interest?

The first step to calculating an imputed interest amount is to determine the principal balance of the loan or bond.

For this simplified example, the constant principal is $500,000.00 and the stated rate is0%.

Choose an annual benchmark rate appropriate to the purpose of the estimate.

In this hypothetical example, the benchmark rate is4%; this is not a current AFR quote.

Select the actual accrual period and day-count basis. This simple example uses1460days and a365-day basis.

The selected year fraction is1460/365 =4.

Finally, estimate the interest excess using I = max(0, P × (benchmark% − stated%)/100 × days/basis).

I = 500,000*(4/100)*4 = $80,000.00.

Imputed Interest Calculator screenshot