MATH Monday: The Rule of 72 - Blog - Free Printable

It looks like you've uploaded a worksheet about The Rule of 72, which is a simple formula used to estimate how long it takes for an investment to double based on a fixed annual rate of return. The formula is:

> Years to double = 72 ÷ Interest Rate

Let’s go through the completed table and explain the solutions, then address any remaining questions (some of which are blurred in your image).

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✔ Completed Table:

| Investment | Rate of Return | Years to Double |
|-----------|----------------|------------------|
| Money Market Account | 1.5% | 48 years |
| International Mutual Fund | 13.9% | 5 years |
| Savings Account | 0.10% | 720 years |
| Checking Account | 0.01% | 7,200 years |
| 3-Year Certificate of Deposit | 2.0% | 36 years |

Let's verify each using the Rule of 72:

1. Money Market Account:
$ 72 ÷ 1.5 = 48 $ → ✔ 48 years

2. International Mutual Fund:
$ 72 ÷ 13.9 ≈ 5.18 $ → Rounded to 5 years ✔

3. Savings Account:
$ 72 ÷ 0.10 = 720 $ → ✔ 720 years

4. Checking Account:
$ 72 ÷ 0.01 = 7,200 $ → ✔ 7,200 years

5. 3-Year Certificate of Deposit:
$ 72 ÷ 2.0 = 36 $ → ✔ 36 years

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🔍 Now, let’s look at the blurred parts and infer what they might be.

From the visible text, there are likely questions below the table that ask things like:

#### Example Question:
> "What interest rate would you need to double your money in 10 years?"

Using the Rule of 72:
- $ \text{Interest Rate} = 72 ÷ \text{Years to Double} $
- $ 72 ÷ 10 = 7.2\% $

✔ So, you’d need a 7.2% interest rate to double your money in 10 years.

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#### Another possible question:
> "You want to save $10,000 for college. If you invest at 6%, how many years will it take to double?"

Answer:
- $ 72 ÷ 6 = 12 $ years

So, it would take 12 years to double your money at 6%.

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💡 Key Takeaways from the Rule of 72:

- It's a quick approximation tool.
- Works best for interest rates between 6% and 10%.
- Becomes less accurate at very high or very low rates.
- Useful for comparing investments quickly.

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🧠 Why does it work?

The Rule of 72 comes from the compound interest formula:
$$
A = P(1 + r)^t
$$
To double: $ 2 = (1 + r)^t $

Taking logarithms:
$$
t = \frac{\ln(2)}{\ln(1 + r)} \approx \frac{0.693}{r}
$$

But since 72 is divisible by many numbers and close to 69.3, people use 72 for easier mental math.

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✔ Final Summary:

| Investment | Rate | Years to Double (via Rule of 72) |
|----------|------|-------------------------------|
| Money Market | 1.5% | 48 |
| International Mutual Fund | 13.9% | ~5 |
| Savings | 0.10% | 720 |
| Checking | 0.01% | 7,200 |
| CD | 2.0% | 36 |

These values were calculated correctly using:
> Years = 72 ÷ Rate (%)

If you have specific questions from the blurred section (like “How long to double at 8%?”), just let me know — I can help solve them!