₹ 10000, invested at 30% rate of interest per annum, but compounded every four months, will give an amount of ₹ ____ in one уеаг.
A)13270
B)13000
C)13300
D)13310

Options

A. 13270
B. 13000
C. 13300
D. 13310

Answer

To solve the problem of calculating the amount obtained from an investment of ₹10,000 at a 30% annual interest rate, compounded every four months, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the parameters:**
- Principal (P) = ₹10,000
- Annual interest rate (R) = 30%
- Compounding frequency = every 4 months
- Time (T) = 1 year

2. **Calculate the effective interest rate for 4 months:**
- Since the interest is compounded every 4 months, we need to determine the interest rate for this period.
- The annual interest rate is 30%, so for 4 months (which is 1/3 of a year), the interest rate will be:
\[ \text{Rate for 4 months} = \frac{30\%}{3} = 10\% \]

3. **Convert the percentage to a decimal:**
- The decimal equivalent of 10% is:
\[ \text{Decimal rate} = \frac{10}{100} = 0.10 \]

4. **Calculate the amount after the first 4 months:**
- The amount after the first 4 months can be calculated using the formula:
\[ A_1 = P \times (1 + r) = 10000 \times (1 + 0.10) = 10000 \times 1.10 = ₹11,000 \]

5. **Calculate the amount after the second 4 months (8 months total):**
- Now, we take the new principal (A_1) and calculate the amount after the next 4 months:
\[ A_2 = A_1 \times (1 + r) = 11000 \times (1 + 0.10) = 11000 \times 1.10 = ₹12,100 \]

6. **Calculate the amount after the third 4 months (1 year total):**
- Finally, we take the new principal (A_2) and calculate the amount after the last 4 months:
\[ A_3 = A_2 \times (1 + r) = 12100 \times (1 + 0.10) = 12100 \times 1.10 = ₹13,310 \]

### Final Amount:
The total amount after one year is **₹13,310**.

### Answer:
Thus, the correct option is **D) ₹13,310**.