In what time would 5000 amount to 5800 at 8% per annum simple interest ?

Options

A. 2
B. 3
C. 4
D. 5

Answer

To solve the problem of how long it will take for Rs. 5000 to amount to Rs. 5800 at an 8% per annum simple interest rate, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 5000
- Amount (A) = Rs. 5800
- Rate of interest (R) = 8% per annum

### Step 2: Calculate the interest earned
To find the interest (I) earned, we subtract the principal from the amount:
\[ I = A - P \]
\[ I = 5800 - 5000 = 800 \]

### Step 3: Use the formula for simple interest
The formula for calculating simple interest is:
\[ I = \frac{P \times R \times T}{100} \]
Where:
- I = Interest
- P = Principal
- R = Rate of interest
- T = Time in years

### Step 4: Substitute the known values into the formula
We know:
- I = 800
- P = 5000
- R = 8

Now, substituting these values into the formula:
\[ 800 = \frac{5000 \times 8 \times T}{100} \]

### Step 5: Simplify the equation
First, simplify the right side:
\[ 800 = \frac{5000 \times 8 \times T}{100} \]
\[ 800 = \frac{40000 \times T}{100} \]
\[ 800 = 400 \times T \]

### Step 6: Solve for T
Now, divide both sides by 400 to find T:
\[ T = \frac{800}{400} \]
\[ T = 2 \]

### Conclusion
The time required for Rs. 5000 to amount to Rs. 5800 at an 8% per annum simple interest is **2 years**.

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