If you put $5,000 in the stock market, how many years would it take you to triple your money if the market is yielding 12% a year?

We can solve this problem using the formula for compound interest, which is:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ A $ is the amount of money you want after interest.
- $ P $ is the initial principal (your starting amount).
- $ r $ is the annual interest rate (as a decimal).
- $ n $ is the number of times the interest is compounded per year.
- $ t $ is the number of years.

In your case, you want to triple your money, so:

\[
A = 3P = 3 \times 5,000 = 15,000
\]

You are given the interest rate $ r = 12\% = 0.12 $ and assume it's compounded annually ($n = 1$).

The formula simplifies to:

\[
15,000 = 5,000 \left(1 + 0.12\right)^t
\]

Dividing both sides by 5,000:

\[
3 = (1.12)^t
\]

Now, solve for $ t $ using logarithms:

\[
\log(3) = t \log(1.12)
\]

\[
t = \frac{\log(3)}{\log(1.12)}
\]

Using logarithm values:

\[
t = \frac{0.4771}{0.0492} \approx 9.7
\]

It will take approximately **9.7 years** to triple your money with a 12% annual return.

Would you like further clarification or details? 

Here are 5 related questions to explore:
1. How does the compounding frequency (e.g., monthly vs. annually) affect the time to triple your investment?
2. What if the interest rate was lower or higher, such as 8% or 15%? How would that change the result?
3. What if you wanted to quadruple your investment instead of tripling it? How would the time change?
4. How do you calculate the time to double your money with the Rule of 72?
5. What impact would fees or taxes on investment returns have on this calculation?

**Tip**: When investing, remember that real market returns can vary year by year, so projected returns are an average, not guaranteed.

Discover how to calculate the time it takes to triple your investment of $5,000 in the stock market with a 12% annual return using the compound interest formula. This example explains the use of logarithms and exponential growth, suitable for students in Grades 10-12.

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