find the difference in the compound interest of Rs 5000 given half yearly and yearly for 1 year and 3 months at the rate of 8% per annum

To find the difference in compound interest when interest is compounded half-yearly and yearly, we'll calculate the compound interest for both scenarios and then find the difference.

### Given Data:
- Principal (\( P \)) = Rs 5000
- Rate of interest (\( R \)) = 8% per annum
- Time period (\( T \)) = 1 year and 3 months = \( 1 + \frac{3}{12} = 1.25 \) years

### 1. Compound Interest (CI) when compounded yearly:
- \( CI = P \left(1 + \frac{R}{100}\right)^T - P \)

For yearly compounding:
- \( T = 1.25 \) years
- \( R = 8\% \)

\[ CI_{yearly} = 5000 \left(1 + \frac{8}{100}\right)^{1.25} - 5000 \]

### 2. Compound Interest (CI) when compounded half-yearly:
- For half-yearly compounding, the rate per half-year is \( \frac{R}{2} \) and the number of half-years is \( 2T \).

So,
- \( R_{half-yearly} = \frac{8}{2} = 4\% \)
- Number of half-years = \( 2 \times 1.25 = 2.5 \)

\[ CI_{half-yearly} = 5000 \left(1 + \frac{4}{100}\right)^{2.5} - 5000 \]

### 3. Difference between the two compound interests:
\[ \text{Difference} = CI_{half-yearly} - CI_{yearly} \]

Now let's calculate the exact values.### Results:

1. **Compound Interest when compounded yearly**: Rs 504.90
2. **Compound Interest when compounded half-yearly**: Rs 515.10
3. **Difference between the two compound interests**: Rs 10.20

Would you like more details or have any further questions?

Here are 5 related questions:
1. How does the compound interest change if the rate of interest is increased to 10%?
2. What would the compound interest be if the time period were 2 years instead of 1 year and 3 months?
3. How does monthly compounding compare to half-yearly and yearly compounding for the same principal?
4. What is the difference in compound interest for a different principal, say Rs 10,000?
5. How does the difference change if the time period is extended to 3 years?

**Tip:** For investments with more frequent compounding periods (like half-yearly or quarterly), the compound interest will generally be higher compared to less frequent periods (like yearly).

Learn how to find the difference in compound interest when Rs 5000 is invested at 8% per annum for 1 year and 3 months, compounded yearly vs half-yearly. Detailed calculations and results provided.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation