Recalculating interest in an audit
Interest expense and accrued interest are easy to recompute from the agreement, the principal outstanding and the dates. Recalculation is one of the audit procedures, and a clean recomputation is stronger evidence than an analytical expectation. The usual reasons a recomputed figure differs from the books are a different day-count basis, a balance that changed during the period, a rate reset on a floating loan, and interest that was capitalized, prepaid or paid but not recorded. See searching for unrecorded liabilities for the related completeness work.
Formula
Simple interest is I = P × r × t. The year fraction t is the number of days counted in the period divided by the days in the year basis. The first day of the period is counted and the last is not.
Conventions used
- 30/360 (bond basis). ISDA 2006 Definitions section 4.16(f). The first date's day is capped at 30. If that day is then 30, the second date's day is capped at 30 too. Days = 360 × years + 30 × months + days, over 360.
- 30E/360. Section 4.16(g). Both days are capped at 30. This is the Eurobond form.
- Actual/360. Section 4.16(e). Real days over 360.
- Actual/365 (fixed). Section 4.16(d). Real days over 365, in leap years too. For 1 February to 1 April 2005 the fraction is 59/365.
- Actual/Actual (ISDA). Section 4.16(b). Days falling in each calendar year divided by 365 or 366, then added. For 1 November 2003 to 1 May 2004 that is 61/365 + 121/366 = 0.497724.
Limits
The US NASD or SIFMA form of 30/360 adds end-of-February rules that the ISDA bond basis does not; if an agreement or a lender system uses that form, a February period can differ by a day or two. The tool assumes one rate and one balance for the whole period. For a loan with payments, rate changes or compounding, work period by period or use the loan amortization schedule. For the going concern and covenant side of debt, see the DSCR calculator.
Illustrative figures only. Check the result against your firm's methodology before relying on it.
Common questions
How do I calculate accrued interest at year end?
Multiply the principal outstanding by the annual rate and by the fraction of a year since interest was last paid or accrued, using the day-count basis in the agreement. For a $250,000 note at 6.5% accruing from 07/01 to 12/31 on a 30/360 basis, the fraction is 180/360 and the accrual is $8,125.00. Compare the result with the accrued interest in the ledger.
What is the difference between 30/360 and Actual/365?
30/360 treats every month as 30 days and the year as 360, so a full year always counts 360 days. Actual/365 counts the real days in the period over a fixed 365-day year. For the same period they usually differ by a small amount, which on a large balance is a common reason a recomputation does not match the lender statement.
Why does Actual/Actual sometimes give a fraction above one for a year?
The ISDA Actual/Actual method splits the period by calendar year and divides the days in each year by that year's length, 365 or 366. A period that is a full year long and starts mid-year can come out slightly above or below 1.0 because its days are divided by different year lengths. That is how the convention is defined, not an error.
Which day-count basis should I use for a note?
The one in the note agreement. Agreements state their own basis, and both Actual/360 and 30/360 are seen in practice. If the agreement is silent, ask the client how the lender computes interest and check it against a lender statement.
Does this calculate imputed or effective interest?
No. It computes simple interest at the stated rate on a constant balance. A note with no stated rate, or one whose rate is not reasonable, may need interest imputed under ASC 835-30, and discounts or premiums are amortized with the effective interest method. For that, use the bond amortization calculator.
Runs in your browser. The figures you type are not sent to CORAA or stored. Check the result against your firm's methodology before relying on it.