To solve the problem step by step, we need to find the total simple interest for 3 years based on the given compound interest information.
### Step 1: Understand the Given Information
We know:
- Principal (P) = Rs 10,000
- Compound Interest (CI) in 2 years = Rs 1,881
### Step 2: Use the Compound Interest Formula
The formula for compound interest is:
\[
CI = A - P
\]
Where \( A \) is the total amount after the interest is applied.
We can also express the total amount \( A \) using the formula:
\[
A = P \left(1 + \frac{r}{100}\right)^t
\]
Where:
- \( r \) is the annual interest rate
- \( t \) is the time in years
### Step 3: Set Up the Equation
From the information given, we can set up the equation:
\[
A - P = 1881
\]
Substituting for \( A \):
\[
P \left(1 + \frac{r}{100}\right)^2 - P = 1881
\]
### Step 4: Substitute the Principal
Substituting \( P = 10,000 \):
\[
10,000 \left(1 + \frac{r}{100}\right)^2 - 10,000 = 1881
\]
### Step 5: Simplify the Equation
This simplifies to:
\[
10,000 \left(1 + \frac{r}{100}\right)^2 = 10,000 + 1881
\]
\[
10,000 \left(1 + \frac{r}{100}\right)^2 = 11,881
\]
### Step 6: Divide by 10,000
Dividing both sides by 10,000 gives:
\[
\left(1 + \frac{r}{100}\right)^2 = \frac{11,881}{10,000}
\]
\[
\left(1 + \frac{r}{100}\right)^2 = 1.1881
\]
### Step 7: Take the Square Root
Taking the square root of both sides:
\[
1 + \frac{r}{100} = \sqrt{1.1881}
\]
Calculating the square root:
\[
1 + \frac{r}{100} \approx 1.09
\]
### Step 8: Solve for r
Subtracting 1 from both sides:
\[
\frac{r}{100} \approx 0.09
\]
Multiplying by 100:
\[
r \approx 9\%
\]
### Step 9: Calculate Simple Interest for 3 Years
Now we can find the simple interest (SI) using the formula:
\[
SI = \frac{P \times r \times t}{100}
\]
Where:
- \( P = 10,000 \)
- \( r = 9 \)
- \( t = 3 \)
Substituting the values:
\[
SI = \frac{10,000 \times 9 \times 3}{100}
\]
\[
SI = \frac{270,000}{100}
\]
\[
SI = 2700
\]
### Final Answer
The total simple interest in 3 years for the same principal amount with the same annual interest rate is Rs 2,700.
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