Answer :
Sure! Let's break down the problem and solve it step by step.
### Information Given:
1. Principal (P): Rs 2,000
2. Rate of Interest (R): 5% per annum
3. Time (T): 1 year
### Part 1: Calculate Simple Interest
The formula for Simple Interest (SI) is:
[tex]\[ \text{SI} = \frac{P \times R \times T}{100} \][/tex]
Substitute the given values:
[tex]\[ \text{SI} = \frac{2000 \times 5 \times 1}{100} \][/tex]
[tex]\[ \text{SI} = \frac{10000}{100} \][/tex]
[tex]\[ \text{SI} = 100 \][/tex]
So, the Simple Interest for one year is Rs 100.
### Part 2: Calculate Compound Interest (Compounded Annually)
The formula for Compound Interest (CI) when interest is compounded annually is:
[tex]\[ \text{CI} = P \left(1 + \frac{R}{100}\right)^T - P \][/tex]
Substitute the given values:
[tex]\[ \text{CI} = 2000 \left(1 + \frac{5}{100}\right)^1 - 2000 \][/tex]
[tex]\[ \text{CI} = 2000 \left(1 + 0.05\right) - 2000 \][/tex]
[tex]\[ \text{CI} = 2000 \times 1.05 - 2000 \][/tex]
[tex]\[ \text{CI} = 2100 - 2000 \][/tex]
[tex]\[ \text{CI} = 100 \][/tex]
So, the Compound Interest for one year is also Rs 100.
### Conclusion:
Both Simple Interest and Compound Interest for the given sum of Rs 2,000 at an interest rate of 5% per annum over 1 year are the same, amounting to Rs 100.
The reason behind this is that compound interest shows a significant difference from simple interest over multiple periods (years), but for a single period (1 year), they yield the same result. Therefore, in this case, both types of interest are the same.
### Information Given:
1. Principal (P): Rs 2,000
2. Rate of Interest (R): 5% per annum
3. Time (T): 1 year
### Part 1: Calculate Simple Interest
The formula for Simple Interest (SI) is:
[tex]\[ \text{SI} = \frac{P \times R \times T}{100} \][/tex]
Substitute the given values:
[tex]\[ \text{SI} = \frac{2000 \times 5 \times 1}{100} \][/tex]
[tex]\[ \text{SI} = \frac{10000}{100} \][/tex]
[tex]\[ \text{SI} = 100 \][/tex]
So, the Simple Interest for one year is Rs 100.
### Part 2: Calculate Compound Interest (Compounded Annually)
The formula for Compound Interest (CI) when interest is compounded annually is:
[tex]\[ \text{CI} = P \left(1 + \frac{R}{100}\right)^T - P \][/tex]
Substitute the given values:
[tex]\[ \text{CI} = 2000 \left(1 + \frac{5}{100}\right)^1 - 2000 \][/tex]
[tex]\[ \text{CI} = 2000 \left(1 + 0.05\right) - 2000 \][/tex]
[tex]\[ \text{CI} = 2000 \times 1.05 - 2000 \][/tex]
[tex]\[ \text{CI} = 2100 - 2000 \][/tex]
[tex]\[ \text{CI} = 100 \][/tex]
So, the Compound Interest for one year is also Rs 100.
### Conclusion:
Both Simple Interest and Compound Interest for the given sum of Rs 2,000 at an interest rate of 5% per annum over 1 year are the same, amounting to Rs 100.
The reason behind this is that compound interest shows a significant difference from simple interest over multiple periods (years), but for a single period (1 year), they yield the same result. Therefore, in this case, both types of interest are the same.
