Find compound interest on 50000 at 12% per annum for 6 month, compounded quarterly.

Options

A. 3045
B. 2875
C. 3125
D. 2965

Answer

To find the compound interest on ₹50,000 at 12% per annum for 6 months, compounded quarterly, we can follow these steps:

### Step 1: Identify the values
- Principal (P) = ₹50,000
- Rate (R) = 12% per annum
- Time (T) = 6 months

### Step 2: Convert the time into years
Since the interest is compounded quarterly, we need to express the time in years:
- 6 months = 6/12 = 0.5 years

### Step 3: Determine the number of compounding periods
Since the interest is compounded quarterly:
- Number of compounding periods per year = 4
- Total compounding periods (n) for 0.5 years = 0.5 * 4 = 2

### Step 4: Calculate the effective rate per compounding period
The annual interest rate is 12%, so the rate per quarter (R/n) is:
- Rate per quarter = 12% / 4 = 3%

### Step 5: Use the compound interest formula
The formula for compound interest is:
\[ A = P \left(1 + \frac{R}{100n}\right)^{nt} \]
Where:
- A = Amount after time t
- P = Principal
- R = Annual interest rate
- n = Number of times interest is compounded per year
- t = Time in years

Substituting the values into the formula:
\[ A = 50000 \left(1 + \frac{3}{100}\right)^{2} \]

### Step 6: Calculate the amount
First, calculate \( 1 + \frac{3}{100} \):
\[ 1 + \frac{3}{100} = 1.03 \]

Now, raise it to the power of 2:
\[ (1.03)^{2} = 1.0609 \]

Now, multiply by the principal:
\[ A = 50000 \times 1.0609 = 53045 \]

### Step 7: Calculate the compound interest
Compound Interest (CI) is given by:
\[ CI = A - P \]
Substituting the values:
\[ CI = 53045 - 50000 = 3045 \]

### Final Answer
The compound interest on ₹50,000 at 12% per annum for 6 months, compounded quarterly, is ₹3045.

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