# Imputed Interest

## What is an 'Imputed Interest'

Imputed interest is used by the Internal Revenue Service (IRS) as a means of collecting tax revenues on loans or securities that pay little or no interest. Imputed interest is important for discount bonds, such as zero-coupon bonds, and other securities that are sold below face value and mature at par. The IRS uses an accretive method when calculating the imputed interest on Treasury bonds and has Applicable Federal Rates (AFR) that set a minimum interest rate in relation to imputed interest and original issue discount rules.

## BREAKING DOWN 'Imputed Interest'

Imputed interest may apply to loans among family and friends. For example, a mother loans her son \$50,000 with no interest charges. The applicable short-term federal rate is 2%. The son should be paying his mother \$1,000 annually (\$50,000 x .02 = \$1,000.) The Internal Revenue Service (IRS) assumes the mother collects this amount from her son and lists it on her tax return as interest income, even though she did not collect it.

## Applicable Federal Rates

Because many low-interest or interest-free loans were being transacted and not being taxed, the IRS established Applicable Federal Rates (AFR) through the Tax Act of 1984. The AFR determines the lowest interest that may be charged on loans below a specific interest rate threshold and considers the amount of potential income generated from the interest rate as imputed income. Because of the creation of AFR, the IRS may collect tax revenue from loans that otherwise are not taxed.

## Calculating Imputed Interest on a Zero-Coupon Bond

When calculating imputed interest on a zero-coupon bond, an investor first determines the bond’s yield to maturity (YTM). Assuming the accrual period is one year, the investor divides the face value of the bond by the price he paid when purchasing it. He then increases the value by a power equal to one divided by the number of accrual periods before the bond matures. The investor reduces the number by one and multiplies by the number of accrual periods in one year to determine the zero-coupon bond’s YTM.

Because the adjusted purchase price of a zero-coupon bond is initially equal to its purchase price when issued, the accrued interest gained over each accrual period adds to the adjusted purchase price. The accrued interest is the initial adjusted purchase price multiplied by the YTM. This value is the imputed interest for the period.

## Example of Imputed Interest

Imputed interest is important for determining pension payouts. For example, when an employee retires from a company in which he was a member of a pension plan, the company may offer the retiree a lump sum of the \$500,000 set aside for him under the plan, or he may receive \$5,000 a year in benefits. Assuming the applicable short-term federal rate is 2%, the retiree needs to determine whether he may receive a better imputed interest rate in another market by taking the lump sum and purchasing an annuity providing greater income.