The amount received at 8% per annum com pound interest after 2 year is₹ 72,900. What was the principal (in ₹)?

Options

A. 65000
B. 67500
C. 60000
D. 62500

Answer

To find the principal amount when the amount received after 2 years at 8% per annum compound interest is ₹72,900, we can follow these steps:

### Step 1: Understand the formula for compound interest
The formula for the amount \( A \) in compound interest is given by:
\[ A = P \left(1 + \frac{r}{100}\right)^t \]
where:
- \( A \) is the amount after time \( t \),
- \( P \) is the principal amount,
- \( r \) is the rate of interest,
- \( t \) is the time in years.

### Step 2: Identify the known values
From the question, we know:
- \( A = 72,900 \)
- \( r = 8\% \)
- \( t = 2 \) years

### Step 3: Substitute the known values into the formula
We can substitute the known values into the formula:
\[ 72,900 = P \left(1 + \frac{8}{100}\right)^2 \]

### Step 4: Simplify the equation
First, calculate \( 1 + \frac{8}{100} \):
\[ 1 + \frac{8}{100} = 1 + 0.08 = 1.08 \]
Now substitute this back into the equation:
\[ 72,900 = P (1.08)^2 \]

### Step 5: Calculate \( (1.08)^2 \)
Now, calculate \( (1.08)^2 \):
\[ (1.08)^2 = 1.1664 \]
So, we have:
\[ 72,900 = P \times 1.1664 \]

### Step 6: Solve for \( P \)
To find \( P \), we can rearrange the equation:
\[ P = \frac{72,900}{1.1664} \]
Now, perform the division:
\[ P = 62,500 \]

### Conclusion
The principal amount \( P \) is ₹62,500.

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