Ray's New Intellectual Arithmetic · Lesson LXXV · Unit 8: Percentage and interest
75. Finding the principal from the amount
Goal: Your child finds the principal when the principal and interest together are known.
You'll need
- The book page (press “📖 Book page”, or use a printed copy)
- Paper for jotting, though the work is meant to be done in the head
What's in the book
Seven problems. The model: 10 per cent interest makes the amount 11/10 of the principal, so $55 is 11/10 of it and the principal is $50.
The lesson, step by step
Warm up
Ask three or four problems from the last lesson again, out of order. Your child answers and says why.
Show the reasoning
Say2 years at 5 per cent is 10 per cent, so the amount is the principal and a tenth more: eleven-tenths. Eleven-tenths are $55, so one-tenth is $5, and the principal is $50.
Work the problems aloud
Read each problem on the page aloud. Your child answers, then explains in a full sentence, the way the book's model solutions do. The problems go like this:
What principal at interest for 2 years at 5 per cent will amount to $55?
A note at interest for 3 years 4 months at 6 per cent now amounts to $30: what was its face?
Two-fifths of A's money at 8% for 2½ years amounts to $60: what is all his money?
Ask “Why?”
After each answer ask “Why?” or “How do you know?” Ray's wants the reasoning said aloud, not just the number. If your child stalls, go back to the model and say the first half of the explanation together.
Wrap up
Pick the two problems that were hardest today. Tomorrow, start with those as the warm-up.
Afterwards
Do the rest of the lesson's problems over the next day or two, a few at a time. Move on when your child can explain them without help.
Answers to the book's problems
1) $50. 2) $200. 3) $500. 4) $250. 5) $300. 6) $25. 7) $125.
Worked out for this site from the scan. If a number in your copy differs, trust the book. Every answer is in Ray's own Key ↗.