A sum of money put at 11% per annum simple interest amounts to Rs. 10370 in 2 years. What will it amount to in 3 years at the same rate?

Answer

To solve the problem step by step, we will follow the process of calculating the principal amount first and then finding the amount after 3 years at the same interest rate.

### Step 1: Understand the given information
- Rate of interest (R) = 11% per annum
- Time (T) = 2 years
- Amount (A) after 2 years = Rs. 10,370

### Step 2: Use the formula for Simple Interest
The formula for Simple Interest (SI) is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- P = Principal amount
- R = Rate of interest
- T = Time in years

### Step 3: Relate Amount, Principal, and Simple Interest
The relationship between Amount, Principal, and Simple Interest is:
\[ A = P + \text{SI} \]
From this, we can express Simple Interest as:
\[ \text{SI} = A - P \]

### Step 4: Set up the equation
From the information given:
\[ \text{SI} = \frac{P \times 11 \times 2}{100} = \frac{22P}{100} \]
And we know:
\[ A = 10,370 \]
So we can write:
\[ 10,370 = P + \frac{22P}{100} \]

### Step 5: Combine the terms
To combine the terms, we can express \( P \) in terms of a common denominator:
\[ 10,370 = P + \frac{22P}{100} \]
This can be rewritten as:
\[ 10,370 = \frac{100P + 22P}{100} \]
\[ 10,370 = \frac{122P}{100} \]

### Step 6: Solve for Principal (P)
Now, we can solve for \( P \):
\[ 122P = 10,370 \times 100 \]
\[ 122P = 1,037,000 \]
\[ P = \frac{1,037,000}{122} \]
\[ P = 8,500 \]

### Step 7: Calculate Simple Interest for 3 years
Now that we have the principal, we can calculate the Simple Interest for 3 years:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P = 8,500 \)
- \( R = 11 \)
- \( T = 3 \)

So,
\[ \text{SI} = \frac{8,500 \times 11 \times 3}{100} \]
\[ \text{SI} = \frac{281,500}{100} \]
\[ \text{SI} = 2,815 \]

### Step 8: Calculate the Amount for 3 years
Now, we can find the Amount after 3 years:
\[ A = P + \text{SI} \]
\[ A = 8,500 + 2,815 \]
\[ A = 11,315 \]

### Final Answer
The amount after 3 years at the same rate will be Rs. 11,315.

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