## Accrued Interest Revenue

### Learning Outcomes

• Calculate and record accrued interest

Interest is the fee charged for use of money over a specific time period. To the maker of the note, or borrower, interest is an expense; to the payee of the note, or lender, interest is a revenue. A borrower incurs interest expense; a lender earns interest revenue. The basic formula for computing interest is:

$\text{Principal}\times\text{Interest Rate}\times\text{Frequency of a year}$

Principal is the face value of the note. The interest rate is the annual stated interest rate on the note. Frequency of a year is the amount of time for the note and can be either days or months. We need the frequency of a year because the interest rate is an annual rate and we may not want interest for an entire year but just for the time period of the note.

Most promissory notes have an explicit interest charge, and although some notes are labeled as “zero interest,” there is often a fee built into the note. For instance, a no-interest note might have a face value of $10,000, but the actual proceeds to the borrower are “discounted” to$9,000, meaning that although there is no stated interest, there is $1,000 of interest built-in to the transaction. To show how to calculate interest, assume HWC borrowed$200,000 from Cobalt, Co. on Oct 1, evidenced by a promissory note. The note has a principal (face value) of $200,000, an annual interest rate of 10%, and a life of 90 days. The interest calculation is: $\200,000\text{ principal}\times10\text{% interest rate}\times\left(\dfrac{90\text{ days}}{360\text{ days}}\right)=\5,000$ Note that in this calculation we expressed the time period as a fraction of a 360-day year because the interest rate is an annual rate and the note life was days. If the note life was months, we would divide by 12 months for a year. Sometimes a lender or textbook uses this “bank method”—so called because some banks would use 360 days instead of 365 since that actually results in a higher effective interest rate. The maturity date is the date on which a note becomes due and must be paid. Sometimes notes require monthly installments (or payments) but usually, all the principal and interest must be paid at the same time. The wording in the note expresses the maturity date and determines when the note is to be paid. A note falling due on a Sunday or a holiday is due on the next business day. Examples of the maturity date wording are: • On demand. “On demand, I promise to pay . . . .” When the maturity date is on demand, it is at the option of the holder and cannot be computed. The holder is the payee, or another person who legally acquired the note from the payee. • On a stated date. “On July 18, 2021, I promise to pay . . . .” When the maturity date is designated, computing the maturity date is not necessary. • At the end of a stated period. 1. “One year after date, I promise to pay . . . .” When the maturity is expressed in years, the note matures on the same day of the same month as the date of the note in the year of maturity. 2. “Four months after date, I promise to pay . . . .” When the maturity is expressed in months, the note matures on the same date in the month of maturity. For example, one month from July 18 is August 18, and two months from July 18 is September 18. If a note is issued on the last day of a month and the month of maturity has fewer days than the month of issuance, the note matures on the last day of the month of maturity. A one-month note dated January 31 matures on February 28. 3. “Ninety days after date, I promise to pay . . . . ” When the maturity is expressed in days, the exact number of days must be counted. The first day (date of origin) is omitted, and the last day (maturity date) is included in the count. For example, a 90-day note dated October 19 matures on January 17 of the next year, as shown here: Days Held 12 30 31 17 90Double line This example brings up an interesting revenue recognition issue. Assume the 10% note from HWC to Cobalt in the amount of$200,000 is compounded annually, rather than daily or monthly, just to simplify this next calculation. Let’s also assume Cobalt follows GAAP, which means accrual-based accounting, and the company’s year-end for accounting purposes is December 31. Under the concept of recognizing revenue as earned, and in relation to the economic concept that interest is essentially rent on money, then interest is earned as time passes and should be recognized on the books of Cobalt as revenue even before HWC actually pays the interest in January of next year.

We calculated the total interest that will be due on January 17th, along with the \$200,000 principal, as follows:

$\200,000\text{ principal}\times10\text{% interest rate}\times\left(\dfrac{90\text{ days}}{360\text{ days}}\right)=\5,000$

However, as we are adjusting the books for December 31 to bring the accounts in line with accrual-basis accounting, we would accrue interest income earned to date: 73 days worth:

Days Held 12 30 31 73Double line

$\200,000\text{ principal}\times10\text{% interest rate}\times\left(\dfrac{73\text{ days}}{360\text{ days}}\right)=\4,055.56$

That amount would be the interest earned through December 31, and so we would create an adjusting journal entry to record it:

Date Description Post. Ref. 20– Interest Receivable 4,055.56 Interest Revenue 4,055.56 To record interest earned on note to HWC

That revenue represents interest earned in October, November, and December. The remainder will be recognized in January when the entire amount is paid.

First, a couple of notes. The 360-day-year convention is not used very often anymore since computers have made it easier for banks and companies to calculate interest using actual days (365 or 366, depending on the year). Also, in calculating the due date of a note, start on the day after the date on the note (don’t include that day, but do include the last day). For instance, a 75-day note executed on January 15th would be due on the 31st of March, unless it was a leap year, in which case it would be due on the 30th of March.

days January February 16 16 28 29 31 30 75Double line 75Double line

In January, the clock starts ticking on the 16th, which means there is no interest accruing during the first 15 days, just the last 16. Interest accrues all through February, and the note is then due on the 75th day.

Verify this calculation on your own and then try your hand at this one: What is the due date of a 90-day note executed on September 1?

The answer is November 30.