The simple interest accrued in 9 years on a principal of Rs. 24,250 /- is 162 percent of the principal. What is the rate of interest p.c.p.a ?

Options

A. 22
B. 16
C. 18
D. Cannot be determined

Answer

To find the rate of interest per annum (p.c.p.a) based on the given information, we can follow these steps:

### Step 1: Determine the Simple Interest
We know that the simple interest (SI) accrued in 9 years is 162% of the principal amount.

Given:
- Principal (P) = Rs. 24,250
- Simple Interest (SI) = 162% of P

Calculating SI:
\[ SI = \frac{162}{100} \times 24,250 = 39,285 \]

### Step 2: Use the Simple Interest Formula
The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- SI = Simple Interest
- P = Principal
- R = Rate of interest (p.c.p.a)
- T = Time in years

### Step 3: Rearrange the Formula to Solve for R
We need to rearrange the formula to find the rate (R):
\[ R = \frac{SI \times 100}{P \times T} \]

### Step 4: Substitute the Known Values
Now we can substitute the values we have:
- SI = 39,285
- P = 24,250
- T = 9

Substituting these into the equation:
\[ R = \frac{39,285 \times 100}{24,250 \times 9} \]

### Step 5: Calculate R
Now we perform the calculations:
\[ R = \frac{39,285 \times 100}{218,250} \]
\[ R = \frac{3,928,500}{218,250} \approx 18 \]

### Conclusion
The rate of interest per annum (p.c.p.a) is approximately **18%**.

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