You invest $8 today at 19% simple interest per year. In how many years will you have $11? Round to the nearest hundredth using double rounding.

To solve this problem, we can use the formula for simple interest:

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

Where:
- $ A $ is the final amount (which is $11),
- $ P $ is the principal (which is $8),
- $ r $ is the interest rate (which is 19% or 0.19), and
- $ t $ is the time in years (which we need to find).

Rearranging the formula to solve for $ t $:

\[
t = \frac{A - P}{Pr}
\]

Substitute the known values:

\[
t = \frac{11 - 8}{8 \times 0.19}
\]

Now, let's calculate the value of $ t $.The time it will take to accumulate $11 from an $8 investment at 19% simple interest is approximately 1.97 years. After rounding to the nearest hundredth, the answer remains 1.97 years.

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the difference between simple and compound interest?
2. How would the time change if the interest rate were higher, say 25%?
3. How do you calculate the final amount with compound interest?
4. What would be the total amount after 2 years instead of 1.97 years?
5. Can you solve this using continuous compounding?

**Tip:** Simple interest grows at a constant rate, unlike compound interest, which grows exponentially.

Learn how to calculate the time it takes to accumulate $11 from an $8 investment with a 19% simple interest rate. Using the simple interest formula, this problem explains key concepts in interest calculation and algebra. Suitable for students in Grades 7-10.

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