The simple interest on a certain sum of money for 3 years at 5% per annum is Rs 1,200. Find the amount due and the compound interest on this sum of money at the same rate and after 2 years, interest is reckoned annually.

Answer

To solve the problem step by step, we will first find the principal amount using the simple interest formula, then calculate the amount due and the compound interest for the given period.

### Step 1: Find the Principal Amount
Given:
- Simple Interest (SI) = Rs 1200
- Rate (R) = 5% per annum
- Time (T) = 3 years

We use the formula for Simple Interest:
\[ SI = \frac{P \times R \times T}{100} \]
Substituting the known values:
\[ 1200 = \frac{P \times 5 \times 3}{100} \]
This simplifies to:
\[ 1200 = \frac{15P}{100} \]
Multiplying both sides by 100:
\[ 120000 = 15P \]
Now, divide both sides by 15:
\[ P = \frac{120000}{15} = 8000 \]
So, the principal amount \( P \) is Rs 8000.

### Step 2: Calculate the Amount Due Using Compound Interest
Now we need to find the amount due after 2 years using the compound interest formula.

Given:
- Principal (P) = Rs 8000
- Rate (R) = 5%
- Time (T) = 2 years

We use the formula for Compound Interest:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Substituting the known values:
\[ A = 8000 \left(1 + \frac{5}{100}\right)^2 \]
This simplifies to:
\[ A = 8000 \left(1 + 0.05\right)^2 = 8000 \left(1.05\right)^2 \]
Calculating \( (1.05)^2 \):
\[ (1.05)^2 = 1.1025 \]
Now substituting back:
\[ A = 8000 \times 1.1025 = 8820 \]
So, the total amount due \( A \) is Rs 8820.

### Step 3: Calculate the Compound Interest
To find the compound interest (CI), we use the formula:
\[ CI = A - P \]
Substituting the values:
\[ CI = 8820 - 8000 = 820 \]
So, the compound interest is Rs 820.

### Final Results
- Amount due: Rs 8820
- Compound Interest: Rs 820