Ray's New Higher Arithmetic · Arts. 295–296 · Unit 17: Percentage with Time: Interest
78. Finding interest: the common method and aliquot parts
Goal: Your student finds simple interest and amount for years, months and days, by multiplying and by aliquot parts.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Case I: the principle, the common method with a worked problem and general rule, eleven examples (answers printed), then the method by aliquot parts with a worked problem.
The lesson, step by step
Warm-up
What is 6% of $250? (15.) What is 4% of $320? ($12.80.)
The idea
Read:
The interest is equal to the continued product of the principal, rate, and time.
and the remark about months:
Unless otherwise specified, 30 days are considered to make a month;
SayThe book uses a 360-day business year: 12 months of 30 days.
Work the book's example
What is the interest of $320 for 3 yr. 5 mo. 18 da., at 4%?
5 mo. 18 da. = 168 days = 168/360 = 7/15 yr. One year's interest is $12.80; × 3 7/15 = $44.37.
The rule
Read:
Multiply the principal by the rate, and that product by the time expressed in years; the product is the interest.
Add the principal and interest, to find the amount.
Guided practice
Together:
$178.63 for 2 yr. 5 mo. 26 da., at 7%.
$6084.25 for 1 yr. 3 mo., at 4½%.
Check against the printed answers.
Aliquot parts
Show the book's second method on $354.80 for 3 yr. 7 mo. 19 da. at 6%: one year's interest is $21.288. Then 3 yr. = $63.864; 6 mo. = half a year = $10.644; 1 mo. = a sixth of that = $1.774; 18 da. and 1 da. by parts of a month. The total is $77.41.
Independent practice and wrap-up
Your student works more of the eleven examples, using either method. Ask: Which method felt quicker?