Ray's New Higher Arithmetic · Arts. 298–299 · Unit 17: Percentage with Time: Interest
80. Finding the time and the rate
Goal: Your student finds how long a sum must be loaned, and at what rate, to earn a given interest.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Case II (given principal, rate and interest, find the time) and Case III (given principal, interest and time, find the rate), each with a worked problem, a rule and examples. Answers are printed.
The lesson, step by step
Warm-up
Ask: $100 at 5% earns $5 a year. How many years to earn $20? (4.)
Case II: the time
Read:
Given the principal, the rate, and the interest, to find the time.
John Thomas loaned $480, at 5%, till the interest was $150; required the time.
One year's interest is $24. $150 ÷ $24 = 6¼ years = 6 yr. 3 mo.
Rule:
Divide the given interest by the interest of the principal for one year; the quotient is the time.
Guided practice
In what time will any sum treble itself by simple interest, at 4%, 10%, 12%?
Hint: to treble, the interest must be twice the principal, 200%.
Case III: the rate
Read:
Given the principal, interest, and time, to find the rate.
At what rate per cent will $4800 gain $840 interest in 2½ years?
At 1% for 2½ years, $4800 earns $120. $840 ÷ $120 = 7, so the rate is 7%.
Divide the given interest by the interest of the principal for the given time, at 1%.
Guided practice
What is the rate of interest when $35000 yields an income of $175 a month?
Independent practice
Your student works more of the examples from both cases, writing the leftover months as days (one tenth of a month is 3 days).
Check and wrap-up
Check the printed answers. Ask: To double money at 10%, how many years? (10.) At 5%? (20.)