Ray's New Practical Arithmetic · Arts. 187–189 · Unit 17: Interest
90. Finding the principal, and the interest formulas
Goal: Your child finds the principal from the interest (Case IV) or from the amount (Case V), and reads the five interest formulas.
You'll need
- Paper and pencil, or a slate or small whiteboard
What's in the book
Page 235 gives Case IV (Art. 187) with two worked examples and the rule, with problems on page 236. Page 236 gives Case V (Art. 188), and page 237 its problems and the formulas for the five cases (Art. 189).
The lesson, step by step
Warm-up
Ask: At 10% a year, what principal earns $5 in one year?
Case IV
Given the time, per cent and interest, to find the principal.
The interest for 3 yr., at 9%, is $21.60: what is the principal?
In 3 years the interest is .27 of the principal, so the principal is $21.60 ÷ .27 = $80.
Multiply the rate by the time, and divide the interest by the product.
Case V
Given the time, per cent, and amount to find the principal.
What principal in 5 yr., at 6%, will amount to $650?
In 5 years the amount is 1.30 of the principal: $650 ÷ 1.30 = $500.
Multiply the rate by the time, and divide the amount by 1 plus the product.
The formulas
Page 237 lists the formulas with letters: p × r × t = i, and the others turn this around. Copy them onto a card. They are the same idea as the percentage formulas, with time added.
Guided practice
Do these together:
What principal, at 5%, will produce a yearly interest of $1023.75?
The amount for 2 yr. 9 mo., at 8%, is $285.48: what is the principal?
Independent practice and check
Your child works the remaining Case IV and Case V problems on pages 236–237. The book prints the answer at the end of each problem line. Have your child cover the answers with a strip of paper, work the problem, then slide the strip down to check.
Mental-math wrap-up
Aloud: interest $12 for 2 yr. at 6%, principal? amount $110 for 1 yr. at 10%, principal?