Sarita invested Rs. 6250 at the rate 4% per annum for one year. If the interest is compounded halfyearly, then the amount received by Sarita at the end of the year will be:

Options

A. (a) 5000
B. (b) 5250
C. (c) 5002.5
D. (d) 10000

Answer

To solve the problem step by step, we will calculate the amount received by Sarita after investing Rs. 6250 at an interest rate of 4% per annum, compounded half-yearly.

### Step 1: Identify the given values
- Principal (P) = Rs. 6250
- Rate of interest (R) = 4% per annum
- Time (T) = 1 year

### Step 2: Determine the number of compounding periods
Since the interest is compounded half-yearly, we need to find out how many half-year periods are in 1 year.
- Number of half-year periods (N) = 1 year / 0.5 year = 2

### Step 3: Calculate the effective rate per compounding period
The annual rate of interest is 4%. Since the interest is compounded half-yearly, we divide the annual rate by 2.
- Effective rate per half-year = R / 2 = 4% / 2 = 2%

### Step 4: Convert the effective rate into decimal form
To use the formula for compound interest, we convert the percentage into decimal form.
- Effective rate in decimal = 2% = 2 / 100 = 0.02

### Step 5: 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
- N = Number of compounding periods

Substituting the values we have:
\[ A = 6250 \left(1 + 0.02\right)^{2} \]

### Step 6: Calculate the amount
Now, we can calculate:
\[ A = 6250 \left(1.02\right)^{2} \]
\[ A = 6250 \times 1.0404 \] (since \(1.02^2 = 1.0404\))
\[ A = 6502.50 \]

### Step 7: Conclusion
The amount received by Sarita at the end of the year will be Rs. 6502.50.

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