Ray's New Practical Arithmetic · Art. 184 · Unit 17: Interest
88. The twelve per cent method
Goal: Your child finds the interest of $1 at 12% instantly ("months are cents, a third of the days are mills"), then uses it for any rate and any principal.
You'll need
- Paper and pencil, or a slate or small whiteboard
What's in the book
Page 229 explains the 12% method (Art. 184) with problems 1–13. Page 230 extends it to any per cent, and page 231 to any sum, each with worked examples, a rule and problems; a few more are on page 232. Answers are printed.
The lesson, step by step
Warm-up
Ask: 12% a year is how much per month? (1%.) So $1 earns how much a month at 12%? (1 cent.)
The idea
The interest of $1 for any number of months, at 12%, is as many cents as there are months.
3 days is a tenth of a month, so it earns 1 mill. So the rule is:
Call the months cents, and one-third of the days mills.
Try it: $1 for 9 mo. 12 da. is 9 cents and 4 mills, $0.094.
Any per cent
Find the interest, at 12%, and take such a part of this as the given per cent is of 12%.
For 6%, take half. For 8%, take 2/3. For 9%, take 3/4.
Ray's example: $1 for 2 yr. 5 mo. 18 da. at 12% is $0.296, so at 6% it is $0.148.
Any sum
Find the interest of $25, for 1 yr. 5 mo. 18 da., at 6%.
$1 at 12% is $0.176; at 6% it is $0.088; × 25 = $2.20.
Take either factor for the multiplier as is most convenient.
Guided practice
Do these two together:
Of $40, for 6 mo. 21 da., at 6%.
Of $120, for 10 mo. 12 da., at 7%.
Independent practice and check
Your child works a selection from pages 229–231. 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
Interest of $1 at 12%, aloud: 5 mo.; 1 yr. 3 mo.; 2 mo. 15 da.; then at 6%.
Tip
This shortcut was a favorite with bank clerks. Many families find it the most fun part of the interest chapter.