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The problem asks for the number of years it will take for Ludwig's investment of $20,000 USD to grow to $80,000 USD at an interest rate of 6% per annum, compounded annually.

We can use the compound interest formula:

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

Where:
- $A$ is the final amount ($80,000),
- $P$ is the initial principal ($20,000),
- $r$ is the annual interest rate (6% or 0.06),
- $n$ is the number of times the interest is compounded per year (since it is compounded annually, $n = 1$),
- $t$ is the time in years (which we are trying to find).

Rearranging the formula to solve for $t$:

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

Let's calculate this.It will take approximately 23.79 years for Ludwig's investment to grow from $20,000 to $80,000 at a 6% annual interest rate, compounded annually.

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. What if the interest rate was compounded monthly instead of annually?
2. How would the time change if the interest rate was 5% instead of 6%?
3. How much would the investment be worth after 10 years?
4. What formula can be used for continuously compounded interest?
5. How does the future value change with a higher or lower initial principal?

**Tip:** When calculating compound interest, always remember to check how frequently the interest is compounded (e.g., annually, monthly, etc.), as it significantly impacts the growth.

Ludwig invests $20,000 USD at 6% p.a. compounded annually. How many years will it take for his investment to reach $80,000 USD?

Learn how to calculate the number of years it will take for a $20,000 investment to grow to $80,000 at a 6% annual interest rate compounded annually. This problem covers compound interest calculations using logarithms. Suitable for Grades 11-12.

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