Find the difference between CI and SI for 3rd year on 6400 at the rate of 12.5%?

Options

A. ₹200.5
B. ₹210.5
C. ₹ 202.5
D. ₹ 212.5

Answer

To find the difference between Compound Interest (CI) and Simple Interest (SI) for the third year on a principal amount of Rs. 6400 at the rate of 12.5%, we will follow these steps:

### Step 1: Calculate Simple Interest (SI)
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P = 6400 \) (Principal)
- \( R = 12.5 \% = \frac{12.5}{100} = \frac{1}{8} \)
- \( T = 3 \) years

Substituting the values into the formula:
\[ SI = \frac{6400 \times \frac{1}{8} \times 3}{1} = 6400 \times \frac{3}{8} = 2400 \]

### Step 2: Calculate Compound Interest (CI)
To calculate CI for 3 years, we will find the interest for each year separately.

**For Year 1:**
\[ CI_1 = P \times \frac{R}{100} = 6400 \times \frac{12.5}{100} = 6400 \times 0.125 = 800 \]

**For Year 2:**
The principal for Year 2 is the initial principal plus the interest from Year 1:
\[ \text{New Principal} = 6400 + 800 = 7200 \]
\[ CI_2 = 7200 \times \frac{12.5}{100} = 7200 \times 0.125 = 900 \]

**For Year 3:**
The principal for Year 3 is the new principal plus the interest from Year 2:
\[ \text{New Principal} = 7200 + 900 = 8100 \]
\[ CI_3 = 8100 \times \frac{12.5}{100} = 8100 \times 0.125 = 1012.5 \]

### Step 3: Total Compound Interest (CI)
Now, we add the CI for all three years:
\[ CI = CI_1 + CI_2 + CI_3 = 800 + 900 + 1012.5 = 2712.5 \]

### Step 4: Calculate the Difference between CI and SI
Now we find the difference between CI and SI:
\[ \text{Difference} = CI - SI = 2712.5 - 2400 = 312.5 \]

### Final Answer
The difference between Compound Interest and Simple Interest for the third year is **Rs. 312.5**.

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