Calculate the compound interest for the second year on Rs. 15,000 invested for 5 years at 6% per annum.

Answer

To calculate the compound interest for the second year on Rs. 15,000 invested for 5 years at 6% per annum, we will follow these steps:

### Step 1: Calculate the Amount at the End of the First Year
We will use the formula for compound interest to find the amount at the end of the first year. The formula is:

\[ A = P \left(1 + \frac{r}{100}\right)^n \]

Where:
- \( A \) = Amount after time \( n \)
- \( P \) = Principal amount (initial investment)
- \( r \) = Rate of interest per annum
- \( n \) = Time in years

Given:
- \( P = 15,000 \)
- \( r = 6\% \)
- \( n = 1 \)

Substituting the values into the formula:

\[ A = 15,000 \left(1 + \frac{6}{100}\right)^1 \]

Calculating the expression inside the parentheses:

\[ A = 15,000 \left(1 + 0.06\right) \]
\[ A = 15,000 \times 1.06 \]
\[ A = 15,900 \]

### Step 2: Use the Amount from Step 1 as the Principal for the Second Year
The amount at the end of the first year, Rs. 15,900, will be the principal for the second year.

### Step 3: Calculate the Compound Interest for the Second Year
Now, we will calculate the interest for the second year using the same formula for compound interest. Here, the new principal \( P \) is Rs. 15,900, the rate \( r \) remains 6%, and the time \( n \) is 1 year.

Using the formula again:

\[ A = P \left(1 + \frac{r}{100}\right)^n \]

Substituting the values:

\[ A = 15,900 \left(1 + \frac{6}{100}\right)^1 \]
\[ A = 15,900 \left(1 + 0.06\right) \]
\[ A = 15,900 \times 1.06 \]
\[ A = 16,834 \]

### Step 4: Calculate the Compound Interest for the Second Year
The compound interest for the second year is the amount at the end of the second year minus the amount at the end of the first year:

\[ CI = A_{second\ year} - A_{first\ year} \]
\[ CI = 16,834 - 15,900 \]
\[ CI = 934 \]

### Final Answer
The compound interest for the second year is Rs. 954.

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