The Rule of 72

Show your work for each problem.

1.
At 6% annual interest, approximately how many years will it take for an investment to double?
1. a)24 years
2. b)6 years
3. c)12 years
4. d)18 years
Answer: 12 years
Using the Rule of 72: years. This is a quick way to estimate doubling time for compound interest.
2.
Using the Rule of 72, how many years does it take for money to double at 9% interest?
Answer: 8
years. At 9% interest, your money doubles approximately every 8 years.
3.
What interest rate is needed to double your money in 12 years?
1. a)6%
2. b)4%
3. c)8%
4. d)10%
Answer: 6%
Rate = . You need a 6% annual interest rate to double your money in 12 years.
4.
At 4% annual interest, how many years until your money doubles?
Answer: 18
years. Lower interest rates mean longer doubling times.
5.
Bank A offers 4% interest. Bank B offers 8% interest. How many years faster will your money double at Bank B?
Answer: 9
1. Calculate doubling time at Bank A (72/4) 18
2. Calculate doubling time at Bank B (72/8) 9
3. Find the difference (Bank A time - Bank B time) 9
6.
A credit card charges 18% interest. How many years until an unpaid balance doubles?
1. a)6 years
2. b)2 years
3. c)4 years
4. d)8 years
Answer: 4 years
years. High interest rates on debt can be very dangerous - your debt doubles in just 4 years!
7.
If inflation is 3% per year, how many years until prices double?
Answer: 24
years. This means something costing 100 dollars today will cost 200 dollars in 24 years.
8.
You invest 1000 dollars at 8% interest. How much will you have after 27 years?
Answer: 8000
1. Calculate doubling time at 8% 9
2. How many times does money double in 27 years? 3
3. What is 1000 doubled 3 times? (1000 x 2 x 2 x 2) 8000
9.
The Rule of 72 is most accurate for interest rates between:
1. a)1% and 3%
2. b)30% and 50%
3. c)4% and 12%
4. d)15% and 25%
Answer: 4% and 12%
The Rule of 72 is most accurate for rates between 4% and 12%, which covers most common investment scenarios. Outside this range, use the Rule of 69 or the exact formula.
10.
You want to double your money in 8 years. What interest rate do you need? (Enter just the number)
Answer: 9
Rate = . You need a 9% annual return to double your money in 8 years.
11.
You invest 2000 dollars at age 25 with 6% returns. How much will you have at age 61?
Answer: 16000
1. How many years from age 25 to 61? 36
2. What is the doubling time at 6%? 12
3. How many times does money double in 36 years? 3
4. What is 2000 doubled 3 times? 16000
12.
If 1000 dollars becomes 4000 dollars in 18 years, what was the approximate interest rate?
1. a)12%
2. b)4%
3. c)8%
4. d)6%
Answer: 8%
4000/1000 = 4x = 2 doublings. Each doubling took 18/2 = 9 years. Rate = 72/9 = 8%.
13.
A 500 dollar credit card debt at 24% interest is never paid. How much is owed after 9 years?
Answer: 4000
1. What is the doubling time at 24%? 3
2. How many times does debt double in 9 years? 3
3. What is 500 doubled 3 times? 4000
14.
Using the Rule of 114, how many years to TRIPLE money at 6% interest?
Answer: 19
Rule of 114: years to triple. The Rule of 114 is similar to the Rule of 72 but for tripling.
15.
Why does the Rule of 72 use 72 instead of the mathematically exact number (69.3)?
1. a)69.3 is too small
2. b)72 is easier to divide mentally
3. c)Historical tradition only
4. d)72 gives more accurate results
Answer: 72 is easier to divide mentally
72 has many divisors (2, 3, 4, 6, 8, 9, 12) making mental math easier. The slight loss in accuracy is worth the convenience for quick estimates.