Ray's New Higher Arithmetic · Art. 297 · Unit 17: Percentage with Time: Interest
79. The six per cent method and exact interest
Goal: Your student finds interest at 6% by the quick method and adjusts it for other rates; knows how exact interest and the 365-day year differ.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Six per cent methods: the interest on $1 at 6% for years, months and days, two rules, examples (answers printed), notes on exact interest, New York's 365-day year, finding time between dates, and English money.
The lesson, step by step
Warm-up
Ask: At 6% a year, what is the interest on $1 for 1 year? For 2 months? (6 cents; 1 cent.)
The idea
Read:
At 6% per annum, the interest on $1 for 1 year is 6 ct., or .06 of the principal.
SaySo $1 earns 1 cent every 2 months, and 1 mill every 6 days.
Work the book's example
What is the interest of $560 for 3 yr. 8 mo. 12 da., at 6%?
3 yr. → 18 ct.; 8 mo. → 4 ct.; 12 da. → 2 mills. So $1 earns $.222, and $560 earns $.222 × 560 = $124.32.
The second rule
Read:
Reduce the years, if any, to months, and write the whole number of months as decimal hundredths; after which, place ⅓ of the days, if any, as thousandths; multiply half the principal by this number, the product is the interest.
Other rates: 12% is twice the 6% interest, 7% is the 6% interest plus one sixth of it, and so on.
Exact interest
Read:
In New York 365 days are counted a year instead of 360.
In England the actual number of days is counted.
Try:
Find the interest of $7302.85 for 365 da., at 6%, counting 360 da. to a year.
Independent practice
Your student works a selection of the examples, including one in English money if they enjoyed the money tables earlier in the book.
Check and wrap-up
Check the printed answers. Ask: Is interest for 365 days at 360 days to the year a little more or a little less than a year's interest? (A little more.)
Tip
One page of this section could not be read online. If your printed copy shows a short rule between the two six per cent methods, read it together too.