Ray's New Intellectual Arithmetic · Lesson LXXVI · Unit 8: Percentage and interest
76. Finding the time
Goal: Your child finds how long money must be lent to earn a given interest, or to double.
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: one year's interest is $3, so $10 takes 3⅓ years; and at 4 per cent money doubles in 100 ÷ 4 = 25 years.
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$50 at 6 per cent earns $3 a year. To earn $10 takes as many years as 3 is contained in 10: 3⅓ years, or 3 years 4 months.
To double, the interest must reach 100 per cent: at 5 per cent that takes 20 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:
In what time, at 6 per cent, will $50 give $10 interest?
In what time will money double at 2, 3, 5, 6, 8 and 10 per cent?
In what time will money triple at 5%?
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) 3 yr 4 mo. 2) 4 yr. 3) 2 yr 6 mo. 4) 2 yr 8 mo. 6) 6 yr 8 mo. 7) 25 yr. 9) 40 yr. 10) 25 yr; 20 yr.
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 ↗.