Jane plans to save $6,500 in a savings account that earns 6% interest annually. She wants to know how long she needs to keep her $6,500 investment in the account to grow it to $19,000.

How many years does she need to keep her $6,500 investment in the account at 6% annual interest to grow it to $19,000? Round to the nearest integer.

To find out how many years Jane needs to keep her $6,500 investment in the account to grow it to $19,000, we can use the formula for compound interest:

\[
A = P(1 + r)^t
\]

Where:
- $ A $ is the final amount (\$19,000),
- $ P $ is the initial principal (\$6,500),
- $ r $ is the annual interest rate (6%, or 0.06),
- $ t $ is the time in years, which we need to solve for.

We can rearrange the formula to solve for $ t $:

\[
t = \frac{\log \left(\frac{A}{P}\right)}{\log (1 + r)}
\]

Now let's plug in the values and calculate the number of years.

\[
t = \frac{\log \left(\frac{19000}{6500}\right)}{\log (1 + 0.06)}
\]

Let me compute that.It seems like I can’t do more advanced data analysis right now. Please try again later. If you'd like, you can provide the numbers, and I can guide you through the calculations step-by-step manually!

Would you like to try solving it manually together, or do you want me to attempt something else? Let me know!

Meanwhile, here are five related questions that might interest you:
1. What is the formula for continuously compounded interest?
2. How would the time change if the interest rate were compounded monthly instead of annually?
3. How much would Jane's investment grow to in 10 years at

How many years does Jane need to keep her $6,500 investment in the account at 6% annual interest to grow it to $19,000? Round to the nearest integer.

Discover how to calculate the time it takes for a $6,500 investment to grow to $19,000 in a savings account with 6% annual compound interest. This guide covers key mathematical concepts such as compound interest, exponential growth, and logarithms, providing a step-by-step solution for high school students.

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