What is the compound interest on a sum of Rs 13,000 at 15% p.a. in 2 years, if the interest is compounded 8- monthly?

Options

A. Rs 4,404
B. Rs 4, 330
C. Rs 4, 033
D. Rs 4,303

Answer

To find the compound interest on a sum of Rs 13,000 at an interest rate of 15% per annum compounded 8-monthly over 2 years, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Principal (P) = Rs 13,000
- Annual Interest Rate (R) = 15%
- Time (T) = 2 years
- Compounding frequency = 8 months

2. **Convert the annual interest rate to the 8-monthly rate**:
- Since 8 months is two-thirds of a year, we need to find the interest rate for this period.
- Rate for 8 months = (15% * 8/12) = (15% * 2/3) = 10%

3. **Determine the number of compounding periods in 2 years**:
- In 2 years, there are 24 months.
- Number of 8-month periods in 2 years = 24 months / 8 months = 3 periods.

4. **Apply the compound interest formula**:
- 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
- \( r \) = interest rate per period
- \( n \) = number of compounding periods

- Substitute the known values into the formula:
\[ A = 13000 \left(1 + \frac{10}{100}\right)^3 \]

5. **Calculate the amount**:
- Simplify the expression:
\[ A = 13000 \left(1 + 0.1\right)^3 = 13000 \left(1.1\right)^3 \]
- Calculate \( (1.1)^3 \):
\[ (1.1)^3 = 1.331 \]
- Now, calculate \( A \):
\[ A = 13000 \times 1.331 = 17303 \]

6. **Calculate the compound interest**:
- Compound Interest (CI) = Amount (A) - Principal (P):
\[ CI = 17303 - 13000 = 4303 \]

### Final Answer:
The compound interest on a sum of Rs 13,000 at 15% p.a. compounded 8-monthly for 2 years is **Rs 4303**.