In how much time, Rs. 20000 will amount to 24500 at the rate of 5% interest?

Options

A. 3.5 year
B. 5.5 year
C. 4 year
D. 4.5 year

Answer

To solve the problem, we need to find out how much time it will take for Rs. 20,000 to amount to Rs. 24,500 at a rate of 5% simple interest.

### Step-by-step solution:

1. **Identify the given values:**
- Principal (P) = Rs. 20,000
- Amount (A) = Rs. 24,500
- Rate of interest (R) = 5%

2. **Calculate the Simple Interest (SI):**
- The formula for Simple Interest is:
\[ SI = A - P \]
- Substituting the values:
\[ SI = 24,500 - 20,000 = 4,500 \]

3. **Use the Simple Interest formula to find time (T):**
- The formula for Simple Interest is also given by:
\[ SI = \frac{P \times R \times T}{100} \]
- Rearranging the formula to solve for time (T):
\[ T = \frac{SI \times 100}{P \times R} \]

4. **Substituting the known values into the formula:**
- Substituting SI = 4,500, P = 20,000, and R = 5%:
\[ T = \frac{4,500 \times 100}{20,000 \times 5} \]

5. **Calculating the values:**
- First calculate the denominator:
\[ 20,000 \times 5 = 100,000 \]
- Now substitute this back into the equation for T:
\[ T = \frac{450,000}{100,000} = 4.5 \]

6. **Conclusion:**
- Therefore, the time required for Rs. 20,000 to amount to Rs. 24,500 at a rate of 5% is **4.5 years**.