You invest $9 today. After 6 years will you have $16. What simple interest rate did you earn on your investment? Answer as a decimal. Round to the nearest ten thousandth using double rounding.

To determine the simple interest rate earned on the investment, we use the simple interest formula:

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

where:

- $ A $ is the amount after time $ t $ (in dollars).
- $ P $ is the principal (initial investment in dollars).
- $ r $ is the simple interest rate (as a decimal).
- $ t $ is the time the money is invested (in years).

Given values:

- $ A = 16 $ (future value).
- $ P = 9 $ (initial investment).
- $ t = 6 $ years.

Plugging in the values:

\[
16 = 9(1 + 6r)
\]

Now, solve for $ r $:

1. Divide both sides by 9:

   \[
   \frac{16}{9} = 1 + 6r
   \]

2. Simplify:

   \[
   1.7778 \approx 1 + 6r
   \]

3. Subtract 1 from both sides:

   \[
   0.7778 = 6r
   \]

4. Divide by 6:

   \[
   r = \frac{0.7778}{6}
   \]

Calculating $ r $:

\[
r \approx 0.1296333
\]

Double rounding (round once, then round the rounded value):

1. Round to the nearest ten-thousandth:

   \[
   r \approx 0.1296
   \]

2. Round $ 0.1296 $ again to the nearest ten-thousandth:

   \[
   r \approx 0.1296
   \]

The simple interest rate you earned on your investment is approximately **0.1296**.

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Do you need further details or have any questions?

### Related Questions:
1. What is the formula for compound interest, and how does it differ from simple interest?
2. How do you calculate the amount of interest earned if you know the rate, principal, and time?
3. What is the effect of doubling the interest rate on the final amount?
4. How does the investment period impact the amount earned with simple interest?
5. Can the interest rate be negative, and what does that imply?

**Tip:** Double rounding helps to avoid rounding errors and improves accuracy in financial calculations.

Learn how to calculate the simple interest rate earned on a $9 investment that grows to $16 in 6 years. This step-by-step solution uses the simple interest formula A = P(1 + rt) and shows how to solve for the rate with double rounding. Suitable for students in Grades 8-10.

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