Manoj deposited Rs 29400 for 6 years at a simple interset. He got Rs 4200 as interset after 6 years The annual rate of interset was

Options

A. `2(8)/(21)` %
B. `2 (7)/(20)%`
C. `3 (8)/(21)%`
D. `4 (8)/(21) %`

Answer

To find the annual rate of interest for Manoj's deposit, we can follow these steps:

### Step 1: Understand the given information
- Principal (P) = Rs 29,400
- Time (T) = 6 years
- Simple Interest (SI) = Rs 4,200

### Step 2: Calculate the Simple Interest for 1 year
To find the interest earned in one year, we divide the total interest by the number of years.

\[ \text{Interest for 1 year} = \frac{\text{Total Interest}}{\text{Time}} = \frac{4200}{6} = 700 \text{ Rs} \]

### Step 3: Calculate the annual rate of interest
The formula for Simple Interest is:

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

Where:
- SI = Simple Interest
- P = Principal
- R = Rate of interest per annum
- T = Time in years

We can rearrange this formula to solve for R:

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

Substituting the known values into the formula:

\[ R = \frac{4200 \times 100}{29400 \times 6} \]

### Step 4: Simplify the calculation
Calculating the denominator:

\[ 29400 \times 6 = 176400 \]

Now substituting back into the equation for R:

\[ R = \frac{420000}{176400} \]

### Step 5: Perform the division
Now we simplify:

\[ R = \frac{420000 \div 4200}{176400 \div 4200} = \frac{100}{42} \approx 2.38 \]

### Step 6: Convert to percentage
To express R as a percentage, we multiply by 100:

\[ R \approx 2.38 \times 100 \approx 2.38\% \]

Thus, the annual rate of interest is approximately **2.38%**.