Ray's New Practical Arithmetic · Arts. 192–193 · Unit 17: Interest
92. Partial payments
Goal: Your child finds the amount due on a note after several part payments, using the United States Rule and the Mercantile Rule.
You'll need
- Paper and pencil, or a slate or small whiteboard
What's in the book
Page 241 defines partial payments and indorsements (Art. 192). Page 242 quotes the court rule and gives a $1000 note with five payments, worked out on pages 243–244 with two rules. Problems follow on pages 245–246, with the Mercantile Rule (Art. 193) on page 246.
The lesson, step by step
Warm-up
Ask: You owe $100 at 6% a year. After 6 months you pay $20. Should the $20 first pay the interest owed so far, or the $100?
The idea
A partial payment is a sum of money, less than the face, paid on a note.
The receipt of a partial payment is acknowledged by indorsing it on the back of the note.
The court rule says each payment first pays the interest then due, and any extra reduces the principal.
This rule is founded on the principle that neither interest nor payment shall draw interest.
Work the book's example
Note of $1000 dated May 1, 1875, at 6%.
The time from May 1, 1875, to November 25, 1875, is 6 mo. 24 da.;
The interest is $34, and the $134 payment covers it: $1034 − $134 = $900, the new principal.
Go on step by step with the book to $600, then $600 again. The next payment ($25) is less than the interest, so wait for the next payment and add both. The principal becomes $400, and on September 10, 1878, $409 is due.
Mercantile Rule
When partial payments are made on notes and accounts running a year or less, the amount due is commonly found by the MERCANTILE RULE.
Find the amount of the debt to the settlement date, find the amount of each payment to the same date, and subtract.
Guided practice
Do this one together:
A note of $200 is dated January 1, 1875.
It was paid $70 on January 1, 1876; find what is due January 1, 1877, at 6%. Then do problem 1 under the Mercantile Rule (the $320 note) together.
Independent practice and check
Your child works two or three more notes from pages 245–246. The book prints the answer at the end of each problem line. Have your child cover the answers with a strip of paper, work the problem, then slide the strip down to check.
Mental-math wrap-up
Aloud: $500 at 6% for 1 year, then $30 paid. New principal?
Tip
These problems are long. One note per day is plenty. Lay the work out in a table: date, time, interest, payment, new principal.