To find the value of $ P $, $ r $, and $ n $ in a formula, it looks like you're working with a compound interest formula. The general formula for compound interest is:

\[
A = P \left(1 + \frac{r}{100n}\right)^{nt}
\]

Where:
- $ A $ is the amount of money accumulated after $ n $ years, including interest.
- $ P $ is the principal amount (the initial money, which is 10,000 in your case).
- $ r $ is the annual interest rate (20% in your case).
- $ n $ is the number of times that interest is compounded per year.
- $ t $ is the number of years the money is invested or borrowed for.

Since you haven't provided $ t $, I'll assume you're asking for the amount after one year ($ t = 1 $).

Let's plug in the values:

\[
A = 10000 \left(1 + \frac{20}{100 \times 3}\right)^{3 \times 1}
\]

Let's calculate this.The amount $ A $ accumulated after 1 year with a principal of \$10,000, an annual interest rate of 20%, and compounded 3 times a year is approximately **\$12,136.30**.

Would you like any further details or have any questions?

Here are five related questions you might find interesting:

1. How would the amount change if the interest rate were 25% instead of 20%?
2. What would be the accumulated amount after 5 years under the same conditions?
3. How does increasing the number of compounding periods per year affect the total amount?
4. Can you calculate the interest amount earned after one year?
5. What would happen if the interest were compounded continuously?

**Tip:** Compound interest grows faster when compounded more frequently. Compare different compounding frequencies to see the effect on your investment.

Learn how to calculate compound interest with a principal of $10,000, an annual interest rate of 20%, and compounded 3 times per year. Explore the formula and detailed calculation steps to understand how interest accrues over time.

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