Sheela deposited Rs 20000 in a bank, where the interest is credited half-yearly. If the rate of interest paid by the bank is 6% per annum, what amount will she get after 1 year?

Answer

To solve the problem step by step, we will calculate the amount Sheela will receive after 1 year with the given conditions.

### Step 1: Identify the given values
- Principal (P) = Rs 20,000
- Rate of interest (R) = 6% per annum
- Time (T) = 1 year

Since the interest is credited half-yearly, we need to adjust the time and rate accordingly.

### Step 2: Adjust the time and rate
Since the interest is compounded half-yearly:
- Time in half-years = 1 year = 2 half-years
- Rate for half-year = 6% per annum / 2 = 3% per half-year

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

### Step 4: Substitute the values into the formula
Now, substituting the values we have:
- \( P = 20,000 \)
- \( R = 3 \) (for half-yearly)
- \( n = 2 \) (for two half-years)

So, the equation becomes:
\[ A = 20000 \left(1 + \frac{3}{100}\right)^2 \]

### Step 5: Simplify the equation
First, calculate \( 1 + \frac{3}{100} \):
\[ 1 + \frac{3}{100} = 1 + 0.03 = 1.03 \]

Now, substitute this back into the equation:
\[ A = 20000 \times (1.03)^2 \]

### Step 6: Calculate \( (1.03)^2 \)
Now we calculate \( (1.03)^2 \):
\[ (1.03)^2 = 1.0609 \]

### Step 7: Calculate the final amount
Now substitute this value back into the equation:
\[ A = 20000 \times 1.0609 = 21218 \]

### Step 8: Final answer
Therefore, the amount Sheela will receive after 1 year is:
\[ \text{Amount} = \text{Rs } 21,218 \]

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