The simple interest on a certain sum of money at 10% per annum is 6,000 in 2 years. Find the amount due at the end of 3 years and at the same rate of interest compounded annually.

Answer

To solve the problem step by step, we will first find the principal amount using the given simple interest, and then we will calculate the amount due at the end of 3 years using the compound interest formula.

### Step 1: Find the Principal Amount (P)

Given:
- Simple Interest (I) = 6000
- Rate (R) = 10% per annum
- Time (T) = 2 years

We use the formula for simple interest:

\[ I = \frac{P \times R \times T}{100} \]

Rearranging the formula to find P:

\[ P = \frac{I \times 100}{R \times T} \]

Substituting the values:

\[ P = \frac{6000 \times 100}{10 \times 2} \]

Calculating:

\[ P = \frac{600000}{20} = 30000 \]

### Step 2: Calculate the Amount Due at the End of 3 Years (A)

Now that we have the principal amount (P), we can find the amount due at the end of 3 years using the compound interest formula:

\[ A = P \left(1 + \frac{R}{100}\right)^T \]

Here:
- P = 30000
- R = 10%
- T = 3 years

Substituting the values into the formula:

\[ A = 30000 \left(1 + \frac{10}{100}\right)^3 \]

Calculating:

\[ A = 30000 \left(1 + 0.1\right)^3 = 30000 \left(1.1\right)^3 \]

Calculating \(1.1^3\):

\[ 1.1^3 = 1.331 \]

Now substituting back:

\[ A = 30000 \times 1.331 = 39930 \]

### Final Answer

The amount due at the end of 3 years is **39,930**.

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