Ray's New Intellectual Arithmetic · Lesson LXXVII · Unit 8: Percentage and interest
77. Finding the rate
Goal: Your child finds the rate of interest from the principal, interest and time.
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
Ten problems. Models: $24 in 2 years is $12 a year, which is 6 per cent of $200; and money doubling in 20 years earns 100 ÷ 20 = 5 per cent.
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
Say$200 earns $24 in 2 years, so $12 a year. $12 is 12 two-hundredths, or 6 hundredths, of $200: 6 per cent.
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 what rate will $200 give $24 interest in 2 years?
At what rate will $200 amount to $240 in 4 years?
At what rate will money double in 12, 10, 8, 5, 4 and 2 years?
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) 6%. 2) 8%. 3) 5%. 4) 7%. 5) 8%. 6) 7%. 7) 5%. 8) 6%. 9) 5%. 10) 8⅓%, 10%, 12½%, 20%, 25%, 50%.
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 ↗.