Ray's New Intellectual Arithmetic · Lesson LXXIV · Unit 8: Percentage and interest
74. Finding the principal from the interest
Goal: Your child works backwards from the interest to the money lent.
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
Eight problems. The model: 2 years at 6 per cent is 12 per cent of the principal; 12 per cent is $3, so the principal is $25.
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
Say12 per cent of the principal is $3, so 1 per cent is 25 cents, and 100 per cent, the principal, is $25.
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 gives $3 interest in 2 years at 6%?
What principal gives $6 interest in 3 years at 4%?
What sum at 5% will give an income of $200 a year?
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) $25. 2) $50. 3) $60. 4) $75. 5) $140. 6) $240. 7) $350. 8) $4000.
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 ↗.