The compound interest on a sum of ₹15800 for 2 years at 9% per annum, when the interest is compound 8 monthly,is (nearest to a rupee):

Options

A. ₹2992
B. ₹3016
C. ₹3018
D. ₹2956

Answer

To solve the problem of finding the compound interest on a sum of ₹15,800 for 2 years at 9% per annum, compounded every 8 months, we will follow these steps:

### Step 1: Understand the compounding frequency
Since the interest is compounded every 8 months, we need to determine how many compounding periods there are in 2 years.
- In 2 years, there are \( \frac{24 \text{ months}}{8 \text{ months}} = 3 \) compounding periods.

### Step 2: Calculate the effective rate of interest per compounding period
The annual interest rate is 9%. Since the interest is compounded every 8 months, we need to find the interest rate for 8 months:
- The effective interest rate for 8 months is \( \frac{9}{12} \times 8 = 6\% \).

### Step 3: Use the compound interest formula
The formula for compound interest is given by:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Where:
- \( A \) = the amount after time \( n \)
- \( P \) = principal amount (₹15,800)
- \( r \) = interest rate per period (6%)
- \( n \) = number of compounding periods (3)

Substituting the values into the formula:
\[ A = 15800 \left(1 + \frac{6}{100}\right)^3 \]
\[ A = 15800 \left(1.06\right)^3 \]

### Step 4: Calculate \( (1.06)^3 \)
Calculating \( (1.06)^3 \):
\[ (1.06)^3 = 1.191016 \]

### Step 5: Calculate the total amount
Now, substituting back to find \( A \):
\[ A = 15800 \times 1.191016 \approx 18818.05 \]

### Step 6: Calculate the compound interest
The compound interest (CI) is given by:
\[ CI = A - P \]
Substituting the values:
\[ CI = 18818.05 - 15800 = 3018.05 \]

### Step 7: Round to the nearest rupee
The nearest rupee to ₹3018.05 is ₹3018.

### Final Answer
The compound interest on a sum of ₹15,800 for 2 years at 9% per annum, compounded every 8 months, is approximately ₹3018.

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