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 the process of finding the principal amount first and then calculating the compound interest for 3 years.

### Step 1: Calculate the Principal Amount
We know that the formula for Simple Interest (SI) is given by:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \(SI\) = Simple Interest
- \(P\) = Principal Amount
- \(R\) = Rate of Interest per annum
- \(T\) = Time in years

From the question, we have:
- \(SI = 6000\)
- \(R = 10\%\)
- \(T = 2\) years

Substituting the values into the formula:
\[ 6000 = \frac{P \times 10 \times 2}{100} \]
This simplifies to:
\[ 6000 = \frac{20P}{100} \]
\[ 6000 = \frac{P}{5} \]
Multiplying both sides by 5:
\[ P = 6000 \times 5 = 30000 \]

### Step 2: Calculate the Amount after 3 Years
The formula for the Amount (A) in compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]
Where:
- \(A\) = Amount
- \(P\) = Principal Amount
- \(R\) = Rate of Interest per annum
- \(n\) = Number of years

We already calculated \(P = 30000\), \(R = 10\%\), and we need to find \(A\) for \(n = 3\):
\[ A = 30000 \left(1 + \frac{10}{100}\right)^3 \]
This simplifies to:
\[ A = 30000 \left(1 + 0.1\right)^3 = 30000 \left(1.1\right)^3 \]
Calculating \(1.1^3\):
\[ 1.1^3 = 1.331 \]
Thus,
\[ A = 30000 \times 1.331 = 39930 \]

### Step 3: Calculate the Compound Interest
The formula for Compound Interest (CI) is:
\[ CI = A - P \]
Substituting the values we have:
\[ CI = 39930 - 30000 = 9930 \]

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

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