Cogito
Consumer Math · Chapter 3 · Lesson 3
The Rule of 72 and Time
How long until it doubles?
12 problems · about 20 minutes · TEKS M.M.3.C
What this lesson teaches
The student uses the Rule of 72 to estimate doubling time and explains the value of starting early.
- Divide 72 by the rate to estimate years until doubling.
- Doublings compound: four doublings is sixteen times.
- The final doubling is the largest, which is why starting early wins.
Warm Up
Straightforward practice. Get the method working first.
5 problemsAt 12% a year, how many years until money doubles?
Answer 6
Why 6 years.
Why does starting early matter so much?
Answer The final doubling adds more than all the earlier ones combined.
Why An early start buys one more doubling, which is the biggest one.
At 8%, years to double?
Answer 9
Why 72 ÷ 8.
At 9%, years to double?
Answer 8
Why 72 ÷ 9.
At 4%, years to double?
Answer 18
Why 72 ÷ 4.
Build It Up
The same ideas with more to keep track of.
3 problems$5000 after 3 doublings. Amount in dollars?
Answer 40000
Why 5000 × 8.
At 8% over 36 years, how many doublings?
Answer 4
Why 36 ÷ 9.
At 3% inflation, years until prices double?
Answer 24
Why 72 ÷ 3.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsMatch each rate with its doubling time.
Answer 6% a year → About 12 years; 8% a year → About 9 years; 12% a year → About 6 years
Why Divide 72 by each rate.
$2000 after 4 doublings. Amount in dollars?
Answer 32000
Why 2000 × 16.
The Doubling: At 6% a year, how many years until money doubles?
Answer 12 years
Why 12 years.
The Four Doublings: $10000 after 4 doublings. What is the amount, in dollars?
Answer 160000 dollars
Why $160000.