Per diem interest, and why payout statements go wrong

A payout statement is one of the few documents a lender produces that somebody else checks line by line. The borrower's solicitor has every reason to, the numbers are small enough to verify by hand, and a discrepancy of a few dollars produces a phone call that costs more than the discrepancy.

Almost all of those calls come from the per diem. Here are the three places it goes wrong.

1. The day-count basis is a term, not a convention

Per diem interest is the principal, times the annual rate, divided by the number of days in a year. The question is which number of days — and there is more than one right answer.

• 365 — the common default in Canadian mortgage lending
• 360 — used in some commercial facilities, and it produces a larger daily figure on the same rate
• 366 — where the agreement specifies the actual days in a leap year

On $450,000 at 7.25%, a 365-day basis gives $89.38 a day and a 360-day basis gives $90.63. Over a sixty-day payout period the two come to $5,363.01 and $5,437.50 — a difference of $74.49, small enough to look like a rounding error and large enough to be queried.

Which one applies is written into the commitment. It is not a house style, it is not whatever the last statement used, and it is not the calculator's default. Check the file.

2. Rounding once, at the end

The per diem is almost never a round number of cents. $450,000 at 7.25% on a 365-day basis is $89.3835616… a day. Round that to $89.38 and then multiply by thirty and you get $2,681.40. Multiply first and round once and you get $2,681.51.

Eleven cents. Nobody will lose sleep over eleven cents, but the same error over a longer period, on a larger balance, at a higher rate, grows — and more to the point, it is an error the other side can reproduce and you cannot explain. Carry the full precision through the calculation and round the total.

3. Which days you count

Interest running from the 1st to the 31st is thirty days on the usual convention — you count the first day and not the last. Some agreements count both ends, which is thirty-one. That single day is a full day's interest on the whole balance, which on the example above is $89.38.

This is the one most likely to be argued, because both parties can be applying a defensible convention and arriving at different numbers. The answer is in the agreement, and where the agreement is silent, the answer is whichever convention you can point to consistently across every statement you have ever issued.

A fourth, which is not about arithmetic

The per diem is calculated on a balance. If the balance moved during the period — a payment landed, a further advance went out, a discharge fee was capitalised — then one per diem across the whole period is wrong regardless of how carefully the other three decisions were made.

Work each stretch on its own balance and add them. A per diem on a stale balance is the second most common error on a payout statement, and unlike the others it does not produce a small difference. It produces a wrong one.