8,000 were invested at 5% per annum C.I. compounded annually . Find :
the amount at the end of the second year.

Answer

To find the amount at the end of the second year for an investment of ₹8,000 at a compound interest rate of 5% per annum, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = ₹8,000
- Rate of interest (R) = 5%
- Time (n) = 2 years

### Step 2: Use the compound interest formula
The formula for calculating the amount (A) in compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]

### Step 3: Substitute the values into the formula
Substituting the values we have:
\[ A = 8000 \left(1 + \frac{5}{100}\right)^2 \]

### Step 4: Simplify the expression inside the parentheses
Calculating the expression inside the parentheses:
\[ A = 8000 \left(1 + 0.05\right)^2 \]
\[ A = 8000 \left(1.05\right)^2 \]

### Step 5: Calculate \( (1.05)^2 \)
Now calculate \( (1.05)^2 \):
\[ (1.05)^2 = 1.1025 \]

### Step 6: Multiply by the principal
Now, multiply this result by the principal:
\[ A = 8000 \times 1.1025 \]
\[ A = 8820 \]

### Final Answer
The amount at the end of the second year is ₹8,820.

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