Track 18 of 25

Reconstructing the arithmetic

Recompute a month of interest by hand, leg by leg, day count, balance and rate, and check the result against the printed figure.

25 lessons

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The four numbers an interest charge is made fromAn interest line is four inputs multiplied, and the statement usually prints only the product.6 min
Opening balance × rate × days ÷ divisorThe charge is a product, not a rate, and any one of the four factors can be the one that moved.6 min
Why Act/360 produces a larger charge than a 365-day yearYou are charged for every real day at a daily rate built as though the year had only 360.6 min
Reconstructing period 1 of the March statementEleven days at 6.97 percent on the opening balance is the whole of the first printed interest line.6 min
Reconstructing period 2The second line is twenty days at a different rate on the same balance, not a new loan.6 min
Adding the legs and matching the printed totalThe printed total is just the two legs added, and the closing balance is that sum sitting on the opening.6 min
Why a mid-period reset produces two legs, not a blended rateA reset splits the month into two products; a single blended rate is a number you invent afterwards.7 min
The blended effective rate, computed after the factThe rate that reproduces the month is none of the rates that applied during the month.6 min
Daily accrual: the charge that does not wait for the statementInterest exists on the morning of the twelfth, whether or not a statement has been issued.6 min
Capitalisation: where this month's charge sits next monthNext month's opening balance is this month's closing balance, so today's charge is tomorrow's principal.5 min
A draw mid-period: how the legs split furtherA mid-month draw adds a third leg; it does not average the balance and apply one rate.6 min
A repayment mid-periodA repayment cuts the balance on the day it posts, and every later day is a different product.6 min
Reconstructing a 28-day February against a 31-day MarchFebruary is cheaper than March by more than the three missing days, because the rate path differs too.6 min
When the printed figure does not match: roundingThe unrounded product is $3,934.065483, and the printed line is that figure taken to the nearest cent.6 min
When the printed figure does not match: a prior-period adjustmentA line that belongs to February can appear in April, and nothing on April's face will reconstruct it.6 min
Checking the balance chain: open + draws − repayments + interest = closeOpening plus draws minus repayments plus interest is the closing balance, or the residual is the finding.5 min
Accrued interest that is not yet in the printed balanceThe printed balance is a date; accrued interest since that date is already inside the maintenance test.6 min
A spread revision rather than an index resetA spread revision uses the same four-factor product as an index reset, and the statement does not say which it was.6 min
Reconstructing a year of twelve statements, in outlineTwelve statements are twelve products in a chain; the year is the sum, not a twelfth of a quoted rate.7 min
What a leap day does under Act/360Under Act/360 a 29 February is one extra day of charge, identical in size to any other day at that rate.6 min
30/360 against Act/360 on the same MarchThirty over 360 pretends March has thirty days, and the missing thirty-first is a full day's accrual.6 min
The effective annual rate versus the stated rateThe stated rate is a 360-day object; a 365-day year and daily compounding both make the money larger.6 min
Interest as a claim on headroomEleven thousand dollars of interest removes sixteen thousand dollars of headroom, because the test is a ratio.6 min
Full reconstruction of the Halden & Wren March statement, every lineEvery printed money line on the March statement is a product you can rebuild from the four factors.6 min
What agreeing with the printed figure does and does not proveMatching the printed total proves the arithmetic is consistent with the inputs you used, and nothing beyond that.6 min

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