Lesson 7 of 25 · 7 min

Why a mid-period reset produces two legs, not a blended rate

A reset splits the month into two products; a single blended rate is a number you invent afterwards.

A blended rate for March can be written down. It is not what produced the charge. The charge was produced by eleven days at 6.97 percent and twenty days at 7.22 percent, each as its own product. A blend is a single number that would have produced the same total if it had applied on every day. That number is an output, computed in the next lesson, and it matches neither printed rate.

The operational reason for two legs is the reset date. On the morning of 12 March the index is 5.37 percent rather than 5.12 percent. Each following day accrues at 7.22 percent. The days already elapsed do not get restated. There is no mechanism that reaches back to 1 March and rewrites those eleven daily accruals at a compromise figure. The statement's job is to add what already happened.

Weighting the two rates by days looks like a blend and is not the effective rate. (11 × 6.97 + 20 × 7.22) ÷ 31 = 7.1313 percent when you carry enough decimals, and that happens to sit next to the effective rate computed from the dollars. It is still not an input. Nobody charged 7.1313 percent on any morning. The products used 6.97 and 7.22.

The distinction matters the moment the balance also moves. A blend of rates, applied to an average balance, double-averages and misses. Lessons 11 and 12 split a draw and a repayment into three legs for that reason. Two legs is the reset-only case, with the balance held flat.

Key terms

Reset: A change in the rate on a stated date. It ends one leg and begins another; it does not rewrite the first.
Blended rate: A single rate invented after the fact that would have produced the same total. Not a rate that applied on any day.
Day-weighted average: Sum of (rate × days) over legs, divided by the period length. A description of the path, not an input to the products.

Worked example

What applied, against what you can invent

Flat $1,847,220 through March. Reset on 12 March from 6.97 percent to 7.22 percent.

Rate on 1–11 March: 6.97%
Rate on 12–31 March: 7.22%
Day-weighted average: 7.1313%
Header on many statements: 7.22%
Charge produced by the two legs: $11,343.47
Charge if 7.22% had applied all month: $11,484.58

Two rates produced the money. The 7.1313 percent figure describes the path; the 7.22 percent figure describes the last morning.

Check yourself

A statement header shows 7.22 percent and an interest total of $11,343.47 on a flat $1,847,220 March. Why does applying 7.22 percent to 31 days fail, and what does the day-weighted 7.1313 percent represent?

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.