A person invests Rs. 8192 at 15% compounded every 5 months for years. Then find the compound interest.

Options

A. Rs. 1544
B. Rs. 1764
C. Rs. 1634
D. Rs. 1884

Answer

To solve the problem of finding the compound interest on an investment of Rs. 8192 at a rate of 15% compounded every 5 months, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 8192
- Rate (R) = 15% per annum
- Time (T) = 1 year (since we are compounding every 5 months, we need to convert this into the number of compounding periods)

### Step 2: Calculate the number of compounding periods
Since the interest is compounded every 5 months, we can determine how many such periods are there in 1 year:
- 1 year = 12 months
- Number of compounding periods in 1 year = 12 months / 5 months = 2.4

However, since we can only have whole compounding periods, we will consider 2 periods of 5 months each (which is 10 months) for our calculation.

### Step 3: Adjust the rate for the compounding period
The effective rate for each compounding period can be calculated as follows:
- Effective rate for 5 months = (15% / 12 months) * 5 months = 6.25%

### Step 4: Calculate the compound interest
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Where:
- A = the amount after time T
- P = principal amount
- r = rate of interest per period
- n = number of compounding periods

Substituting the values:
- P = 8192
- r = 6.25%
- n = 2

Calculating the amount (A):
\[ A = 8192 \left(1 + \frac{6.25}{100}\right)^2 \]
\[ A = 8192 \left(1 + 0.0625\right)^2 \]
\[ A = 8192 \left(1.0625\right)^2 \]
\[ A = 8192 \times 1.1276 \]
\[ A \approx 9235.52 \]

### Step 5: Calculate the compound interest
Compound Interest (CI) can be calculated as:
\[ CI = A - P \]
\[ CI = 9235.52 - 8192 \]
\[ CI \approx 1043.52 \]

### Step 6: Round off the answer
Since we are looking for a whole number, we can round it to the nearest integer:
\[ CI \approx 1044 \]

### Final Answer
The compound interest is approximately Rs. 1044.