Abhishek invested a certain amount at the rate of 8 % per annum for 5 year and obtained a total Sl of Rs. 3800, had he invested the same amount at the same rate for 2 years at C.I., how much amount would he have obtained as CI at the end of 2 year?

Options

A. Rs. 1520
B. Rs. 1550.5
C. Rs. 1550
D. Rs. 1580.8

Answer

To solve the problem step by step, let's break it down:

### Step 1: Calculate the Principal Amount
We know that the formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \(SI\) = Simple Interest
- \(P\) = Principal Amount
- \(R\) = Rate of Interest (per annum)
- \(T\) = Time (in years)

Given:
- \(SI = 3800\)
- \(R = 8\%\)
- \(T = 5\) years

Substituting the values into the formula:
\[ 3800 = \frac{P \times 8 \times 5}{100} \]

### Step 2: Rearranging to Find Principal
Rearranging the equation to solve for \(P\):
\[ P = \frac{3800 \times 100}{8 \times 5} \]
Calculating the denominator:
\[ 8 \times 5 = 40 \]
Now substituting back:
\[ P = \frac{3800 \times 100}{40} \]
Calculating:
\[ P = \frac{380000}{40} = 9500 \]

### Step 3: Calculate Compound Interest (CI) for 2 Years
Now, we will calculate the amount using the formula for Compound Interest:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where:
- \(A\) = Amount after time \(T\)
- \(P\) = Principal Amount (which we found to be 9500)
- \(R\) = Rate of Interest (8%)
- \(T\) = Time (2 years)

Substituting the values:
\[ A = 9500 \left(1 + \frac{8}{100}\right)^2 \]
Calculating \(1 + \frac{8}{100}\):
\[ 1 + 0.08 = 1.08 \]
Now substituting back:
\[ A = 9500 \times (1.08)^2 \]
Calculating \((1.08)^2\):
\[ (1.08)^2 = 1.1664 \]
Now substituting back:
\[ A = 9500 \times 1.1664 = 11080.8 \]

### Step 4: Calculate Compound Interest (CI)
Now we find the Compound Interest:
\[ CI = A - P \]
Substituting the values:
\[ CI = 11080.8 - 9500 \]
Calculating:
\[ CI = 1580.8 \]

### Final Answer
The amount obtained as Compound Interest at the end of 2 years is **Rs. 1580.8**.

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