The simple interest on a sum of money at 4% per annum for 2 years is Rs 80. The compound interest on the same sum for the same period is = ?

Options

A. Rs. 82.60
B. Rs. 82.20
C. Rs. 81.80
D. Rs. 81.60

Answer

To solve the problem of finding the compound interest on a sum of money given the simple interest, we can follow these steps:

### Step 1: Understand the Given Information
We know:
- Simple Interest (SI) = Rs 80
- Rate of Interest (R) = 4% per annum
- Time (T) = 2 years

### Step 2: Use the Simple Interest Formula
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where \( P \) is the principal amount.

### Step 3: Rearrange the Formula to Find Principal (P)
From the formula, we can rearrange it to find \( P \):
\[ P = \frac{SI \times 100}{R \times T} \]
Substituting the known values:
\[ P = \frac{80 \times 100}{4 \times 2} \]
\[ P = \frac{8000}{8} = 1000 \]
So, the principal amount \( P \) is Rs 1000.

### Step 4: Calculate Compound Interest (CI)
The formula for Compound Interest is:
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]
Substituting the values we have:
\[ CI = 1000 \left(1 + \frac{4}{100}\right)^2 - 1000 \]
\[ CI = 1000 \left(1 + 0.04\right)^2 - 1000 \]
\[ CI = 1000 \left(1.04\right)^2 - 1000 \]

### Step 5: Calculate \( (1.04)^2 \)
Now calculate \( (1.04)^2 \):
\[ (1.04)^2 = 1.0816 \]
So, substituting this back:
\[ CI = 1000 \times 1.0816 - 1000 \]
\[ CI = 1081.6 - 1000 \]
\[ CI = 81.6 \]

### Step 6: Conclusion
The compound interest on the same sum for the same period is Rs 81.6.

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