A sum of Rs.14,000 amounts to Rs.22,400 in 12 years at the rate of simple interest. What is the rate of interest?

Options

A. 0.07
B. 0.06
C. 0.05
D. 0.04

Answer

To find the rate of interest for the given problem, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 14,000
- Amount (A) = Rs. 22,400
- Time (T) = 12 years

### Step 2: Calculate the Simple Interest (SI)
The formula for Simple Interest is:
\[ \text{SI} = A - P \]
Substituting the values:
\[ \text{SI} = 22,400 - 14,000 = 8,400 \]

### Step 3: Use the Simple Interest formula to find the rate (R)
The formula for Simple Interest is also given by:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
We can rearrange this formula to find R:
\[ R = \frac{\text{SI} \times 100}{P \times T} \]

### Step 4: Substitute the known values into the formula
Substituting the values we have:
\[ R = \frac{8,400 \times 100}{14,000 \times 12} \]

### Step 5: Simplify the calculation
Calculating the denominator:
\[ 14,000 \times 12 = 168,000 \]
Now substituting this back:
\[ R = \frac{8,400 \times 100}{168,000} \]

### Step 6: Calculate R
Calculating the fraction:
\[ R = \frac{840,000}{168,000} \]
Now simplifying this:
\[ R = 5 \]

### Step 7: Convert R to percentage
Since R is in percentage, we write:
\[ R = 5\% \]

Thus, the rate of interest is **5%**.

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