Simple interest on a certain sum of money for 3 years at 5% per annum is rupes 600. find the amount due and compound interest on this sum at the same rate after 3 years. The interest being reckoned annually.

Answer

To solve the problem, we will follow these steps:

### Step 1: Identify the given values
- Simple Interest (SI) = Rs. 600
- Time (t) = 3 years
- Rate of Interest (R) = 5% per annum

### Step 2: Calculate the Principal (P) using the Simple Interest formula
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times t}{100} \]
Rearranging the formula to find the Principal (P):
\[ P = \frac{SI \times 100}{R \times t} \]
Substituting the known values:
\[ P = \frac{600 \times 100}{5 \times 3} \]

### Step 3: Calculate the Principal
Calculating the above expression:
\[ P = \frac{60000}{15} = 4000 \]
So, the Principal (P) is Rs. 4000.

### Step 4: Calculate the Amount due (A) using the Compound Interest formula
The formula for the Amount (A) when compounded annually is:
\[ A = P \left(1 + \frac{R}{100}\right)^t \]
Substituting the values:
\[ A = 4000 \left(1 + \frac{5}{100}\right)^3 \]
This simplifies to:
\[ A = 4000 \left(1 + 0.05\right)^3 = 4000 \left(1.05\right)^3 \]

### Step 5: Calculate \( (1.05)^3 \)
Calculating \( (1.05)^3 \):
\[ (1.05)^3 = 1.157625 \]
Now substituting back to find A:
\[ A = 4000 \times 1.157625 \]

### Step 6: Calculate the Amount (A)
Calculating the above:
\[ A \approx 4630.50 \]
So, the Amount due after 3 years is approximately Rs. 4630.50.

### Step 7: Calculate the Compound Interest (CI)
The formula for Compound Interest is:
\[ CI = A - P \]
Substituting the values:
\[ CI = 4630.50 - 4000 \]
Calculating the above:
\[ CI = 630.50 \]
So, the Compound Interest after 3 years is Rs. 630.50.

### Final Results:
- Amount due after 3 years: Rs. 4630.50
- Compound Interest after 3 years: Rs. 630.50

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