Find the amount and the compound interest on Rs. 16,000 in 3 years at 10% per annum.

Answer

To solve the problem of finding the amount and compound interest on Rs. 16,000 in 3 years at a 10% per annum interest rate, we will follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 16,000
- Rate of interest (r) = 10% per annum
- Time (n) = 3 years

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

### Step 3: Substitute the values into the formula
Substituting the known values into the formula:
\[ A = 16000 \left(1 + \frac{10}{100}\right)^3 \]

### Step 4: Simplify the expression inside the brackets
First, calculate \( \frac{10}{100} \):
\[ \frac{10}{100} = 0.1 \]
So, we have:
\[ A = 16000 \left(1 + 0.1\right)^3 \]
\[ A = 16000 \left(1.1\right)^3 \]

### Step 5: Calculate \( (1.1)^3 \)
Now, calculate \( (1.1)^3 \):
\[ (1.1)^3 = 1.1 \times 1.1 \times 1.1 = 1.331 \]

### Step 6: Calculate the amount (A)
Now substitute back to find the amount:
\[ A = 16000 \times 1.331 \]
\[ A = 21296 \]

### Step 7: Calculate the compound interest (CI)
The formula for compound interest is:
\[ CI = A - P \]
Substituting the values we found:
\[ CI = 21296 - 16000 \]
\[ CI = 5296 \]

### Final Results
- Amount (A) = Rs. 21,296
- Compound Interest (CI) = Rs. 5,296

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