At what rate will a sum increase by 25% in 2 years at S.I ?

Options

A. 12 1/2
B. 12
C. 10 1/2
D. can't be determined

Answer

To solve the problem of determining the rate at which a sum will increase by 25% in 2 years at simple interest (S.I.), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find the rate of interest (R) that will cause a principal amount (P) to increase by 25% over 2 years.

2. **Define the Principal Amount**: Let's assume the principal amount (P) is 100. This makes calculations easier.

3. **Calculate the Total Amount After 2 Years**:
- If the principal is 100, then a 25% increase means the total amount after 2 years will be:
\[ \text{Total Amount} = P + \text{Increase} = 100 + 25 = 125 \]

4. **Use the Simple Interest Formula**: The formula for simple interest is:
\[ A = P + SI \]
where \( SI = \frac{P \times R \times T}{100} \).
Here, \( A \) is the total amount, \( P \) is the principal, \( R \) is the rate of interest, and \( T \) is the time in years.

5. **Substitute Known Values**: We know:
- \( A = 125 \)
- \( P = 100 \)
- \( T = 2 \)

Plugging these values into the formula gives:
\[ 125 = 100 + \frac{100 \times R \times 2}{100} \]

6. **Simplify the Equation**:
\[ 125 = 100 + 2R \]
Subtract 100 from both sides:
\[ 25 = 2R \]

7. **Solve for R**:
\[ R = \frac{25}{2} = 12.5 \]

8. **Conclusion**: The rate of interest required to achieve a 25% increase in 2 years at simple interest is **12.5%**.

### Final Answer:
The rate at which a sum will increase by 25% in 2 years at simple interest is **12.5%**.

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