Ray's New Intellectual Arithmetic · Lesson LXXVIII · Unit 8: Percentage and interest

78. Present worth and discount

Goal: Your child finds what a debt due in the future is worth now.

⏱ About 20 minutes · 5 steps

Open it at the Internet Archive ↗

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

A note explaining that discount is like interest paid in advance: present worth is like the principal, and the debt due is like the amount. Twelve problems; the model finds a $72 debt due in 4 years at 5 per cent worth $60 now.

The lesson, step by step

  1. Warm up

    Ask three or four problems from the last lesson again, out of order. Your child answers and says why.

  2. Show the reasoning

    SayIn 4 years at 5 per cent, $1 grows to $1.20. So a debt of $72 then is worth as many dollars now as 1.20 is contained in 72, which is $60. The discount is $12.

    It is Lesson LXXV turned into a real question: what is a future payment worth today?

  3. 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 are the present worth and discount of $72 due in 4 years at 5%?

    What is the discount at 6% on $496 due in 4 years?

    What is the present worth at 6% of $77 due in 6 years 8 months?

  4. 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.

  5. 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) present worth $60, discount $12. 2) $400; $120. 3) $25; $5. 4) $500; $250. 5) $45. 6) $96. 7) $4. 8) $50. 9) $44. 10) $55.

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 ↗.

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