The amount that Ram will pay on Rs. 8000 at the rate of 10% per annum compounded half-yearly for `1 (1)/(2)` yr is

Options

A. Rs. 9261
B. Rs. 8000
C. Rs. 4200
D. None of these

Answer

To solve the problem of finding the amount that Ram will pay on Rs. 8000 at the rate of 10% per annum compounded half-yearly for 1.5 years, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 8000
- Rate of interest (R) = 10% per annum
- Time (T) = 1.5 years

### Step 2: Adjust the rate and time for half-yearly compounding
Since the interest is compounded half-yearly:
- The effective rate per half-year = \( \frac{10\%}{2} = 5\% \)
- The number of half-year periods in 1.5 years = \( 1.5 \times 2 = 3 \) half-years

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

### Step 4: Substitute the values into the formula
Substituting the values we have:
\[ A = 8000 \left(1 + \frac{5}{100}\right)^3 \]
\[ A = 8000 \left(1 + 0.05\right)^3 \]
\[ A = 8000 \left(1.05\right)^3 \]

### Step 5: Calculate \( (1.05)^3 \)
Now we need to calculate \( (1.05)^3 \):
\[ (1.05)^3 = 1.05 \times 1.05 \times 1.05 \]
Calculating step-by-step:
1. \( 1.05 \times 1.05 = 1.1025 \)
2. \( 1.1025 \times 1.05 = 1.157625 \)

### Step 6: Calculate the final amount
Now substitute back into the amount formula:
\[ A = 8000 \times 1.157625 \]
Calculating this gives:
\[ A = 9261 \]

### Conclusion
Therefore, the amount that Ram will pay is Rs. 9261.

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