Ray's New Practical Arithmetic · Art. 183 (5th) · Unit 17: Interest
87. Interest for years, months and days
Goal: Your child finds interest when the time is given in years, months and days, by adding parts (first method) or by turning the time into years (second method).
You'll need
- Paper and pencil, or a slate or small whiteboard
What's in the book
Page 226 starts the case "When the Time is Years, Months, and Days" with a worked example. Page 227 solves it a second way, gives Rule I, then the Second Method with Rule II. Problems with printed answers follow on page 228.
The lesson, step by step
Warm-up
Ask: What part of a year is 7 months? 2 months 20 days? (Count 30 days to a month.)
First method
Find the interest of $360 for 2 yr. 7 mo. 25 da., at 8%.
One year: $28.80. Two years: $57.60. 7 months (7/12 of a year): $16.80. 25 days (5/6 of a month): $2. Total $76.40.
Find the interest for each period, and add the results.
Second method
Find the interest of $120 for 4 yr. 6 mo. 20 da., at 6%.
20 da. = 2/3 mo.; 6⅔ mo. = 5/9 yr.; so the time is 4 5/9 yr.
$120 × .06 × 4 5/9 = $32.80.
Reduce the months and days to the fraction of a year.
Multiply the principal by the rate, and multiply the product by the time expressed in years.
Guided practice
Pick two problems from page 228. Have your child do the first by the first method and the second by the second method, then say which felt easier.
Independent practice and check
Your child works about eight more of the problems on page 228. 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 on $100 at 6% for 1 yr. 6 mo.; for 2 yr. 2 mo.
Tip
The book says to "indicate the operation" and cancel before multiplying. Writing $120 × 6/100 × 41/9 and cancelling is much quicker than long decimals.