The simple interest accrued in 8 years on a principal of Rs. 22,500/- is 128 percent of the principal. What is the rate of interest p.c.p.a. ?

Options

A. 14
B. 18
C. 16
D. Cannot be determined

Answer

To solve the problem step by step, we will follow the information provided and use the relevant formulas.

### Step 1: Understand the given information
- Principal (P) = Rs. 22,500
- Time (T) = 8 years
- Simple Interest (SI) = 128% of Principal

### Step 2: Calculate the Simple Interest (SI)
To find the Simple Interest, we first need to calculate 128% of the principal amount.

\[ SI = \frac{128}{100} \times P \]
\[ SI = \frac{128}{100} \times 22,500 \]
\[ SI = 1.28 \times 22,500 \]
\[ SI = 28,800 \]

### Step 3: Use the Simple Interest formula to find the Rate of Interest (R)
The formula for Simple Interest is:

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

Rearranging the formula to find the rate of interest (R):

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

### Step 4: Substitute the values into the formula
Now, we substitute the values we have calculated and given:

\[ R = \frac{28,800 \times 100}{22,500 \times 8} \]

### Step 5: Calculate R
First, calculate the denominator:

\[ 22,500 \times 8 = 180,000 \]

Now, substitute this back into the equation for R:

\[ R = \frac{28,800 \times 100}{180,000} \]
\[ R = \frac{2,880,000}{180,000} \]
\[ R = 16 \]

### Conclusion
The rate of interest per annum (p.c.p.a) is **16%**.

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