At what % of simple interest does an amount of money double in 12 years 

To determine the percentage of simple interest required for an amount of money to double in 12 years, we can use the formula for simple interest:

\[
A = P(1 + rt)
\]

Where:
- \( A \) is the final amount,
- \( P \) is the principal amount,
- \( r \) is the annual interest rate (as a decimal),
- \( t \) is the time in years.

Since the amount doubles, \( A = 2P \). Substituting into the formula:

\[
2P = P(1 + rt)
\]

Dividing both sides by \( P \):

\[
2 = 1 + rt
\]

Solving for \( rt \):

\[
rt = 1
\]

Now, substitute \( t = 12 \) years:

\[
r \times 12 = 1
\]

\[
r = \frac{1}{12}
\]

\[
r = 0.0833
\]

To express \( r \) as a percentage, multiply by 100:

\[
r = 8.33\%
\]

Thus, the required simple interest rate is **8.33% per year**.

Would you like more details, or do you have any other questions?

Here are some related questions for further exploration:
1. What would be the required interest rate if the money doubles in 10 years?
2. How does the formula for compound interest differ in this scenario?
3. What if the money needed to triple in 12 years—what interest rate would be required?
4. How long would it take to double an amount at 6% simple interest?
5. Can the simple interest formula be rearranged to find time \( t \)?

**Tip:** Simple interest grows linearly over time, unlike compound interest, which grows exponentially.

At what % of simple interest does an amount of money double in 12 years?

Learn how to calculate the simple interest rate required to double an amount of money in 12 years using the formula A = P(1 + rt). This problem involves basic algebra and interest calculations, suitable for students in Grades 7-9.

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