Vineet invests a sum of Rs. 41250 at the rate of `5%` per annum. What compound interest will he obtain at the end of 3 years ?

Options

A. Rs. 8100.10
B. Rs. 6502.03
C. Rs. 8210.70
D. Rs. 7879.04

Answer

To find the compound interest that Vineet will obtain at the end of 3 years on his investment of Rs. 41,250 at a rate of 5% per annum, we can follow these steps:

### Step 1: Identify the formula for Compound Interest
The formula to calculate 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)
- \( r \) = Rate of interest per annum
- \( n \) = Number of years

### Step 2: Substitute the values into the formula
Here,
- \( P = 41250 \)
- \( r = 5 \)
- \( n = 3 \)

Substituting these values into the formula gives:
\[ A = 41250 \left(1 + \frac{5}{100}\right)^3 \]

### Step 3: Simplify the expression inside the parentheses
Calculating \( 1 + \frac{5}{100} \):
\[ 1 + \frac{5}{100} = 1 + 0.05 = 1.05 \]

### Step 4: Raise the result to the power of 3
Now, we need to calculate \( (1.05)^3 \):
\[ (1.05)^3 = 1.157625 \] (You can use a calculator for this step)

### Step 5: Calculate the total amount (A)
Now, substitute back into the equation:
\[ A = 41250 \times 1.157625 \]
Calculating this gives:
\[ A \approx 47752.50 \]

### Step 6: Calculate the Compound Interest (CI)
The compound interest can be calculated using the formula:
\[ CI = A - P \]
Substituting the values we found:
\[ CI = 47752.50 - 41250 \]
Calculating this gives:
\[ CI \approx 6502.50 \]

### Final Answer
The compound interest Vineet will obtain at the end of 3 years is approximately Rs. 6502.50.

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