The rate schedule versus a single printed rate

A rate schedule is a list of stated rates with the dates each one applied. A single printed rate is one number, usually the rate in force at period end. They answer different questions. The schedule reconstructs the charge. The single rate describes the last day. Track 5 lesson 11 is the general case; this lesson is that case on a page that, unusually, prints the schedule.

Halden & Wren prints both stated rates: 6.97% for the first eleven days, 7.22% for the last twenty. It also prints the two index fixings, the spread, and the reset date. A thinner statement would print 7.22% once, at the top, and one interest total. That thinner page is the common object. This fixture is the uncommon one that lets you see what the common object hides.

The effective rate for the month — the single rate that would have produced $11,343.47 over 31 days on $1,847,220.00, Act/360 — is not either printed rate. Rearrange the charge: $11,343.47 × 360 ÷ ($1,847,220 × 31) = 0.071313, or 7.1313%. The day-weighted mix is the same number: (0.0697 × 11 + 0.0722 × 20) ÷ 31 = 2.2107 ÷ 31 = 0.071313. Neither 6.97% nor 7.22% equals 7.1313%. A reader who multiplies the closing rate across all 31 days is not using a number the page even printed as a month rate. They are extending a point-in-time rate across a window it did not own.

When a statement prints only the closing rate, the interest total is still a schedule in disguise. Recovering the schedule requires the reset date and the prior rate, which that page does not give.