What is difference between compound interest on 7 5000 for 2 yr at 4% per annum when the interest is compounded yearly and half-yearly?

Answer

To solve the problem of finding the difference between compound interest on ₹75,000 for 2 years at 4% per annum when compounded yearly and half-yearly, we will follow these steps:

### Step 1: Calculate Compound Interest when Compounded Yearly

**Formula for Compound Interest:**
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Where:
- \( A \) = Amount after time \( n \)
- \( P \) = Principal amount (initial investment)
- \( r \) = Rate of interest per annum
- \( n \) = Number of years

**Given:**
- \( P = 75,000 \)
- \( r = 4\% \)
- \( n = 2 \)

**Calculation:**
\[ A = 75000 \left(1 + \frac{4}{100}\right)^2 \]
\[ A = 75000 \left(1 + 0.04\right)^2 \]
\[ A = 75000 \left(1.04\right)^2 \]
\[ A = 75000 \times 1.0816 \]
\[ A = 81012 \]

**Compound Interest (CI) when compounded yearly:**
\[ CI = A - P = 81012 - 75000 = 6012 \]

### Step 2: Calculate Compound Interest when Compounded Half-Yearly

**When compounded half-yearly, the rate and time are adjusted:**
- The rate per half year = \( \frac{4}{2} = 2\% \)
- The number of half-year periods in 2 years = \( 2 \times 2 = 4 \)

**Calculation:**
\[ A = 75000 \left(1 + \frac{2}{100}\right)^4 \]
\[ A = 75000 \left(1 + 0.02\right)^4 \]
\[ A = 75000 \left(1.02\right)^4 \]
\[ A = 75000 \times 1.08243216 \]
\[ A \approx 81182.41 \]

**Compound Interest (CI) when compounded half-yearly:**
\[ CI = A - P = 81182.41 - 75000 = 6182.41 \]

### Step 3: Find the Difference Between the Two Compound Interests

**Difference:**
\[ \text{Difference} = CI_{\text{half-yearly}} - CI_{\text{yearly}} \]
\[ \text{Difference} = 6182.41 - 6012 \]
\[ \text{Difference} = 170.41 \]

### Final Answer:
The difference between the compound interest when compounded yearly and half-yearly is **₹170.41**.

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