Akash invested Rs 48000 at the rate of 15% per annum for one year. If the interest is compounded half-yearly, then find the amount received by Akash after one year.

Options

A. Rs 58470
B. Rs 47470
C. Rs 55470
D. Rs 45470

Answer

To solve the problem step by step, we will calculate the amount received by Akash after one year when the interest is compounded half-yearly.

### Step 1: Identify the given values
- Principal (P) = Rs 48,000
- Rate of interest (R) = 15% per annum
- Time (T) = 1 year

### Step 2: Adjust the rate and time for half-yearly compounding
Since the interest is compounded half-yearly, we need to adjust the rate and time:
- Half-yearly rate = R / 2 = 15% / 2 = 7.5%
- Time in half-years = 1 year = 2 half-years

### Step 3: Use the compound interest formula
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Where:
- \( A \) = Amount after time \( T \)
- \( P \) = Principal
- \( r \) = Rate of interest per period
- \( n \) = Number of periods

### Step 4: Substitute the values into the formula
Substituting the values we have:
- \( P = 48,000 \)
- \( r = 7.5 \)
- \( n = 2 \)

So,
\[ A = 48000 \left(1 + \frac{7.5}{100}\right)^2 \]

### Step 5: Calculate the expression inside the parentheses
\[ 1 + \frac{7.5}{100} = 1 + 0.075 = 1.075 \]

### Step 6: Raise the result to the power of 2
Now calculate:
\[ (1.075)^2 = 1.075 \times 1.075 = 1.155625 \]

### Step 7: Calculate the final amount
Now substitute back into the formula:
\[ A = 48000 \times 1.155625 \]

Calculating this gives:
\[ A = 48000 \times 1.155625 = 55,470 \]

### Final Answer
The amount received by Akash after one year is Rs 55,470.

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