Ray's New Practical Arithmetic · Arts. 185–186 · Unit 17: Interest
89. Finding the time and finding the rate
Goal: Your child finds how long money was lent, and at what rate, when the other numbers are known.
You'll need
- Paper and pencil, or a slate or small whiteboard
What's in the book
Page 232 gives Case II (Art. 185), finding the time, with three worked examples. Page 233 has the rule and problems. Page 234 gives Case III (Art. 186), finding the rate, and page 235 the rest of its problems. Answers are printed.
The lesson, step by step
Warm-up
Ask: $100 earns $6 a year. How many years to earn $18?
Finding the time
Given the principal, the per cent and the interest, to find the time.
The interest of $225 for a certain time, at 4%, was $66: what was the time?
One year's interest is $9; 66 ÷ 9 = 7⅓ years = 7 yr. 4 mo.
Divide the given interest by the interest of the principal for one year.
Doubling
In what time, at 8%, will any principal double itself?
A principal has doubled itself when the interest becomes 100%.
100 ÷ 8 = 12½ years.
Finding the rate
Given the principal, the time and the interest, to find the per cent.
A merchant paid $30 interest for the use of $300, for 1 yr. 8 mo.: what was the per cent?
1 yr. 8 mo. = 5/3 yr. One year's interest is $18, and $18 is 6% of $300.
Find the interest for one year, and find what per cent this is of the principal.
Guided practice
Do these two together:
I lent $200, at 6%, and received $36 interest: how long was the money lent?
At what per cent will any principal double itself in 20 yr?
Independent practice and check
Your child works the problems on pages 233 and 234–235. 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: at 5%, how long to double? at 10%? $100 earned $12 in 2 years: rate?