Lesson 15 of 20 · 8 min

How to recompute an interest leg by hand

Four inputs, one loop, one comparison. It takes ten minutes and it is the only way to verify a charge.

This is the mechanical core of the track. Everything up to here explained why a printed interest figure cannot be taken on trust; this lesson is the procedure for checking it.

The four inputs you need, all from documents you have:

The day-count convention, from the agreement: 360, 365, or 30/360.
The rate or rates in force during the period, and the dates they changed.
The balance on each day of the period, which means the opening balance plus every draw and repayment with its date.
The number of days in the period, from the statement's date range.

interest = Σ over days of [ balance(day) × rate(day) ÷ basis ]

balance(day): What was outstanding on that specific day, including previously capitalised interest.
rate(day): The annual rate in force on that day. Not the period average and not the printed closing rate.
basis: 360 or 365, from the agreement. Using the wrong one produces a 1.39% error.
Σ over days: Add the daily figures. In practice, group days into segments where balance and rate were both constant.

The practical shortcut is segmentation. You rarely need 31 separate calculations — you need one per segment during which both the balance and the rate were constant. A period with one draw and one rate change has three segments, and three multiplications is a ten-minute job.

Then compare. An exact match means the charge is consistent with the terms as stated. A gap of about 1.4 percent means a day-count mismatch. A small gap in either direction usually means a rate segment you did not know about. A large gap means something else, and now you have a specific figure to ask about rather than a vague concern.

Key terms

Segment: A run of days during which both the balance and the rate were constant. Segmenting turns a daily loop into a few multiplications.
Balance-days: Balance multiplied by the number of days it was outstanding. The natural unit for interest arithmetic and for reverse-engineering adjustments.
Reconciliation: Comparing your computed figure with the charged figure. The size and direction of any gap identifies its likely cause.

Worked example

A full recomputation with a draw and a rate change

31-day period. Opening balance $300,000. A $10,000 draw on day 13. Rate 6.85% days 1–12, 7.10% days 13–31. Act/360.

Segment 1: days 1–12, $300,000 at 6.85%: $685.00
Segment 2: days 13–31, $310,000 at 7.10%: $1,161.64
Total computed interest: $1,846.64
Same period computed at 7.10% throughout on $310,000: $1,895.31
Same period computed on an Act/365 basis: $1,821.02
Statement figure to compare against: Should match $1,846.64

Two multiplications produced the answer. The two wrong methods each produce a plausible-looking figure, and each is wrong for a different, identifiable reason.

Check yourself

A 31-day period: $300,000 for the first 12 days at 6.85%, $310,000 for the remaining 19 days at 7.10%, Act/360. What is the interest, and what would using 365 instead do?

Saved in this browser only. No account, nothing sent anywhere.

Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.