The compound interest on Rs 5000 at 8% per annum for 2 years, compounded annually, is

Options

A. RS 800
B. RS 825
C. RS 832
D. RS 850

Answer

To find the compound interest on Rs 5000 at an interest rate of 8% per annum for 2 years, compounded annually, we can follow these steps:

### Step 1: Identify the formula for Compound Interest
The formula for calculating the amount (A) after n years with compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
where:
- \( P \) = principal amount (initial investment)
- \( r \) = annual interest rate (in percentage)
- \( n \) = number of years

### Step 2: Substitute the values into the formula
Here, we have:
- \( P = 5000 \)
- \( r = 8 \)
- \( n = 2 \)

Substituting these values into the formula gives us:
\[ A = 5000 \left(1 + \frac{8}{100}\right)^2 \]

### Step 3: Calculate the value inside the parentheses
First, calculate \( \frac{8}{100} \):
\[ \frac{8}{100} = 0.08 \]
Now, add 1 to this value:
\[ 1 + 0.08 = 1.08 \]

### Step 4: Raise the result to the power of n
Now we need to raise \( 1.08 \) to the power of 2:
\[ 1.08^2 = 1.1664 \]

### Step 5: Calculate the total amount (A)
Now, multiply this result by the principal amount:
\[ A = 5000 \times 1.1664 = 5832 \]

### Step 6: Calculate the compound interest (CI)
The compound interest can be found by subtracting the principal from the total amount:
\[ CI = A - P \]
Substituting the values we have:
\[ CI = 5832 - 5000 = 832 \]

### Final Answer
The compound interest on Rs 5000 at 8% per annum for 2 years, compounded annually, is Rs 832.

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