Ray's New Intellectual Arithmetic · Lesson LXXIX · Unit 8: Percentage and interest
79. Interest puzzles
Goal: Your child reasons about how interest, principal, rate and time relate to each other.
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
Fourteen problems with no model solution, such as what part of the principal the interest is, and when two loans give the same interest.
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
SayAt 6 per cent for 4 years 2 months, the interest is 25 per cent, which is one-fourth of the principal.
Then: 4 years at 10 per cent is 40 per cent; at 5 per cent that takes 8 years.
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:
At 6 per cent, for 4 years 2 months, what part of the principal is the interest?
In what time will money at 5 per cent give the same interest as in 4 years at 10 per cent?
The interest on A's and B's money is $40, and A has twice as much as B: what has each?
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) ¼. 2) ⅕ of the amount. 11) 8 years.
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 ↗.