Mohd. Aslam purchased a house from Avas Vikas Parishad on credit. If the cost of the house is Rs 125000 and the Parishad charges interest at 12% per annum compounded half-yearly, find the interest paid by Aslam after a year and half.

Options

A. Rs `89877`
B. Rs `20000`
C. Rs `28887`
D. Rs `23877`

Answer

To solve the problem step by step, we will calculate the compound interest paid by Mohd. Aslam after a year and a half on the cost of the house which is Rs. 125,000 at an interest rate of 12% per annum compounded half-yearly.

### Step 1: Identify the given values
- Principal (P) = Rs. 125,000
- Rate of interest (R) = 12% per annum
- Time (T) = 1.5 years

### Step 2: Convert the rate and time for half-yearly compounding
Since the interest is compounded half-yearly:
- The effective rate for half-yearly compounding is \( R/2 = 12\%/2 = 6\% \) per half-year.
- The total number of half-year periods in 1.5 years is \( 1.5 \times 2 = 3 \) half-years.

### Step 3: Use the compound interest formula
The formula for the amount (A) when interest is compounded is given by:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]
Where:
- \( P \) = Principal
- \( R \) = Rate of interest per period
- \( n \) = Number of compounding periods

Substituting the values into the formula:
\[ A = 125000 \left(1 + \frac{6}{100}\right)^3 \]

### Step 4: Simplify the expression
Calculate \( 1 + \frac{6}{100} = 1 + 0.06 = 1.06 \). Now, we can rewrite the equation:
\[ A = 125000 \times (1.06)^3 \]

### Step 5: Calculate \( (1.06)^3 \)
Calculating \( (1.06)^3 \):
\[ (1.06)^3 = 1.191016 \]
Now substituting this back into the equation for A:
\[ A = 125000 \times 1.191016 \]

### Step 6: Calculate the total amount
Calculating the amount:
\[ A = 125000 \times 1.191016 \approx 148876.95 \]

### Step 7: Calculate the compound interest (CI)
The compound interest is given by:
\[ CI = A - P \]
Substituting the values:
\[ CI = 148876.95 - 125000 \approx 23876.95 \]

### Final Answer
Therefore, the compound interest paid by Mohd. Aslam after a year and a half is approximately Rs. 23,876.95.

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