Certain simple interest is received on 5000 at certain rate of interest in certain time period. If time period is increased by 4 years then interest is increased by 200 at same rate of interest then find the rate of intetest?

Options

A. `2%`
B. `1%`
C. `1.5%`
D. `0.5%`

Answer

To solve the problem step by step, we will use the formula for Simple Interest (SI) and the information provided in the question.

### Step 1: Understand the given information
We have:
- Principal (P) = 5000
- Increase in time (T) = 4 years
- Increase in interest = 200

### Step 2: Write the formula for Simple Interest
The formula for Simple Interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- SI = Simple Interest
- P = Principal
- R = Rate of interest
- T = Time in years

### Step 3: Calculate the increase in interest due to the increase in time
When the time is increased by 4 years, the increase in Simple Interest is given as 200. This means:
\[ \text{SI for 4 years} = 200 \]

### Step 4: Find the SI for 1 year
Since the increase in interest for 4 years is 200, we can find the interest for 1 year:
\[ \text{SI for 1 year} = \frac{200}{4} = 50 \]

### Step 5: Set up the equation for 1 year SI
Using the formula for Simple Interest for 1 year:
\[ \text{SI for 1 year} = \frac{P \times R \times 1}{100} \]
Substituting the known values:
\[ 50 = \frac{5000 \times R}{100} \]

### Step 6: Solve for R
To find R, we can rearrange the equation:
\[ 50 = \frac{5000R}{100} \]
Multiplying both sides by 100:
\[ 5000R = 5000 \]
Now, divide both sides by 5000:
\[ R = \frac{5000}{5000} = 1 \]

### Step 7: Conclusion
The rate of interest (R) is 1%.