Simple Interest received by a person in 10 years on a principal of Rs. 9500 is 130% of the principal. What is the rate of interest (in %) per annum?

Options

A. 12
B. 13
C. 15
D. 19

Answer

To find the rate of interest per annum, we can follow these steps:

### Step 1: Calculate the Simple Interest
The problem states that the simple interest received in 10 years is 130% of the principal amount.

1. **Principal (P)** = Rs. 9500
2. **Simple Interest (SI)** = 130% of Principal = 130/100 * 9500

\[ SI = \frac{130}{100} \times 9500 = 1.3 \times 9500 = 12350 \]

### Step 2: Use the Simple Interest Formula
The formula for Simple Interest is:

\[ SI = \frac{P \times R \times T}{100} \]

Where:
- \( SI \) is the Simple Interest
- \( P \) is the Principal
- \( R \) is the Rate of Interest per annum
- \( T \) is the Time in years

### Step 3: Substitute the Known Values
From the information we have:
- \( SI = 12350 \)
- \( P = 9500 \)
- \( T = 10 \)

Substituting these values into the formula:

\[ 12350 = \frac{9500 \times R \times 10}{100} \]

### Step 4: Simplify the Equation
To simplify, we can multiply both sides by 100 to eliminate the fraction:

\[ 12350 \times 100 = 9500 \times R \times 10 \]

This simplifies to:

\[ 1235000 = 95000R \]

### Step 5: Solve for R
Now, we can solve for \( R \):

\[ R = \frac{1235000}{95000} \]

Calculating this gives:

\[ R = 13 \]

### Final Answer
Thus, the rate of interest per annum is **13%**.

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