What will be the amount received on `Rs. 25000` at the rate of `20%` per annum compounded yearly for 4 years?

Options

A. `Rs. 51840`
B. `Rs. 50350`
C. `Rs. 53550 `
D. `Rs. 48750`

Answer

To find the amount received on Rs. 25,000 at a rate of 20% per annum compounded yearly for 4 years, we can use the formula for compound interest:

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

Where:
- \( A \) = the amount after time \( n \)
- \( P \) = principal amount (initial investment)
- \( r \) = annual interest rate (in percentage)
- \( n \) = number of years the money is invested or borrowed

### Step 1: Identify the values
- Principal \( P = 25000 \)
- Rate \( r = 20\% \)
- Time \( n = 4 \) years

### Step 2: Substitute the values into the formula
\[ A = 25000 \left(1 + \frac{20}{100}\right)^4 \]

### Step 3: Simplify the expression inside the parentheses
\[ A = 25000 \left(1 + 0.20\right)^4 \]
\[ A = 25000 \left(1.20\right)^4 \]

### Step 4: Calculate \( (1.20)^4 \)
To calculate \( (1.20)^4 \):
\[ (1.20)^4 = 1.20 \times 1.20 \times 1.20 \times 1.20 \]
Calculating step by step:
- \( 1.20 \times 1.20 = 1.44 \)
- \( 1.44 \times 1.20 = 1.728 \)
- \( 1.728 \times 1.20 = 2.0736 \)

So, \( (1.20)^4 = 2.0736 \)

### Step 5: Substitute back to find \( A \)
\[ A = 25000 \times 2.0736 \]

### Step 6: Calculate the final amount
\[ A = 25000 \times 2.0736 = 51840 \]

### Final Answer
The amount received after 4 years will be **Rs. 51,840**.

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