A certain amount of money doubles in 6 years at simple interest. What is the annual rate of interest?

To determine the annual rate of interest when a certain amount of money doubles in 6 years at simple interest, we can use the formula for simple interest:

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

Where:
- $A$ is the total amount after time $t$,
- $P$ is the principal amount (initial investment),
- $r$ is the rate of interest per year (in decimal),
- $t$ is the time in years.

Since the amount doubles, we have:

\[
A = 2P
\]

Substituting this into the formula gives:

\[
2P = P(1 + r \cdot 6)
\]

Dividing both sides by $P$ (assuming $P \neq 0$):

\[
2 = 1 + 6r
\]

Subtracting 1 from both sides:

\[
1 = 6r
\]

Dividing by 6:

\[
r = \frac{1}{6} \approx 0.1667
\]

To convert this to a percentage:

\[
r \approx 16.67\%
\]

Thus, the annual rate of interest is approximately **16.67%**.

Would you like further details or have any questions? Here are some related questions to consider:

1. What would the total amount be after 12 years at this interest rate?
2. How does the interest rate affect the time taken for an investment to double?
3. What are the differences between simple interest and compound interest?
4. If the principal was $1,000, how much interest would be earned in 6 years?
5. How would you calculate the interest if the amount was tripling instead of doubling? 

**Tip:** Always ensure to understand the difference between simple and compound interest as they affect the growth of investments differently.

Discover how to calculate the annual rate of interest when a certain amount of money doubles in 6 years at simple interest. This solution demonstrates the formula for simple interest and provides step-by-step calculations to find the rate of approximately 16.67%. Ideal for students in Grades 7-9.

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