The simple interest on a certain sum of money at 10% per annum is 6,000 in 2 years. Find the compound interest earned in 3 years.

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Find the Principal Amount (P)
We know that the simple interest (SI) formula is given by:
\[ SI = \frac{P \times r \times t}{100} \]
Where:
- \( SI = 6000 \) (given)
- \( r = 10\% \) (given)
- \( t = 2 \) years (given)

We can rearrange the formula to find \( P \):
\[ P = \frac{SI \times 100}{r \times t} \]
Substituting the values:
\[ P = \frac{6000 \times 100}{10 \times 2} \]
Calculating:
\[ P = \frac{600000}{20} = 30000 \]

### Step 2: Calculate the Amount (A) after 3 Years using Compound Interest Formula
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^t \]
Where:
- \( P = 30000 \) (calculated in Step 1)
- \( r = 10\% \) (given)
- \( t = 3 \) years (we need to find the amount after 3 years)

Substituting the values:
\[ A = 30000 \left(1 + \frac{10}{100}\right)^3 \]
This simplifies to:
\[ A = 30000 \left(1 + 0.1\right)^3 = 30000 \left(1.1\right)^3 \]
Calculating \( (1.1)^3 \):
\[ (1.1)^3 = 1.1 \times 1.1 \times 1.1 = 1.331 \]
Now substituting back:
\[ A = 30000 \times 1.331 = 39930 \]

### Step 3: Calculate the Compound Interest (CI)
The compound interest is given by:
\[ CI = A - P \]
Substituting the values:
\[ CI = 39930 - 30000 = 9930 \]

### Final Answer
The compound interest earned in 3 years is **9930**.

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