The difference between simple and compound interest compounded annually on a certain sum of 10000 is 64 for 2 years. Find the interest?

Options

A. a. 8%
B. b. 64%
C. c. 4%
D. d. 2%

Answer

To solve the problem step by step, we will follow the given information and apply the relevant formulas for simple interest (SI) and compound interest (CI).

### Step 1: Understand the problem
We know that the difference between the compound interest and simple interest for 2 years on a principal amount of 10,000 is 64. We need to find the rate of interest (R).

### Step 2: Use the formula for the difference between CI and SI
The formula for the difference between compound interest and simple interest for 2 years is given by:
\[ \text{Difference} = \frac{P \cdot R^2}{100^2} \]
where:
- \( P \) = Principal amount
- \( R \) = Rate of interest

### Step 3: Substitute the known values into the formula
From the problem, we have:
- Difference = 64
- Principal \( P = 10,000 \)

Substituting these values into the formula gives:
\[ 64 = \frac{10,000 \cdot R^2}{100^2} \]

### Step 4: Simplify the equation
Now, simplify the equation:
\[ 64 = \frac{10,000 \cdot R^2}{10,000} \]
This simplifies to:
\[ 64 = R^2 \]

### Step 5: Solve for R
To find \( R \), take the square root of both sides:
\[ R = \sqrt{64} \]
Calculating the square root gives:
\[ R = 8 \]

### Step 6: Conclusion
The rate of interest is:
\[ \text{Rate of Interest} = 8\% \]