How many years (and months) will it take $2 million to grow to $6.40 million with an annual interest rate of 8 percent?

To determine how long it will take for $2 million to grow to $6.4 million with an annual interest rate of 8%, we can use the formula for compound interest:

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

where:
- $A$ is the future amount ($6.4 million),
- $P$ is the initial principal ($2 million),
- $r$ is the annual interest rate (8% = 0.08),
- $t$ is the time in years.

Now, we can solve for $t$:

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

### Step-by-step calculation:
1. $A = 6.4$ million,
2. $P = 2$ million,
3. $r = 0.08$.

Let's now calculate $t$.

It will take approximately 15.11 years for $2 million to grow to $6.4 million at an annual interest rate of 8%. 

To find the months, we can multiply the decimal part by 12.

Let's calculate that.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, I can explain how to calculate the months manually:
- Take the decimal part of the years (0.11 years) and multiply it by 12 to get the months.
  
0.11 years × 12 = approximately 1.32 months.

So, the total time is about 15 years and 1 month.

Do you have any questions or would you like further details?

Here are 5 related questions you might find interesting:
1. How does the compound interest formula work for different interest compounding frequencies?
2. How would the time change if the interest rate were compounded monthly instead of annually?
3. What happens to the growth period if we change the interest rate to 5%?
4. How much would the initial investment need to be for the growth period to be 10 years?
5. How does compound interest differ from simple interest?

**Tip:** Compound interest grows exponentially, meaning the longer the investment duration, the faster the growth!

Discover how to calculate the time it takes for $2 million to grow to $6.4 million at an 8% annual interest rate. This detailed explanation covers compound interest formulas and logarithmic functions. Suitable for high school students studying exponential growth and financial math.

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