What is the compound interest on a sum of Rs 12,000 at 18% per annum for 1`1/3` years, if the interest is compounded 8monthly?

Options

A. `4,708.8`
B. `2,980.2`
C. `33,840.40`
D. `3,052.80`

Answer

To calculate the compound interest on a sum of Rs 12,000 at an interest rate of 18% per annum for 1 and 1/3 years, compounded 8-monthly, we can follow these steps:

### Step 1: Convert the time period into months
1 and 1/3 years can be converted into months:
- 1 year = 12 months
- 1/3 year = 4 months
- Total time = 12 months + 4 months = 16 months

### Step 2: Determine the number of compounding periods
Since the interest is compounded every 8 months, we need to find out how many compounding periods are in 16 months:
- Number of compounding periods = Total months / Compounding frequency
- Number of compounding periods = 16 months / 8 months = 2

### Step 3: Calculate the interest rate per compounding period
The annual interest rate is 18%. Since the interest is compounded every 8 months, we need to calculate the interest rate for this period:
- Interest rate for 8 months = (18% / 12 months) * 8 months = 12%

### Step 4: Use the compound interest formula
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Where:
- \( A \) = the amount of money accumulated after n periods, including interest.
- \( P \) = principal amount (initial investment).
- \( r \) = annual interest rate (as a percentage).
- \( n \) = number of compounding periods.

Substituting the values:
- \( P = 12000 \)
- \( r = 12 \) (interest rate for 8 months)
- \( n = 2 \) (number of compounding periods)

\[ A = 12000 \left(1 + \frac{12}{100}\right)^2 \]
\[ A = 12000 \left(1 + 0.12\right)^2 \]
\[ A = 12000 \left(1.12\right)^2 \]
\[ A = 12000 \times 1.2544 \]
\[ A = 15053.28 \]

### Step 5: Calculate the compound interest
Compound Interest (CI) is calculated as:
\[ CI = A - P \]
\[ CI = 15053.28 - 12000 \]
\[ CI = 3053.28 \]

### Final Answer
The compound interest on a sum of Rs 12,000 at 18% per annum for 1 and 1/3 years, compounded 8-monthly, is Rs 3053.28.

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