What is the sum (in Rs) of money which will become Rs 29160 at the rate of 8% per annum at compound interest in two years?

Options

A. 25000
B. 26000
C. 28000
D. 20000

Answer

To find the sum of money (principal, P) that will become Rs 29,160 at the rate of 8% per annum compounded annually over 2 years, we can use the formula for compound interest:

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

Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial sum of money).
- \( R \) is the annual interest rate (in percentage).
- \( D \) is the number of years the money is invested or borrowed.

Given:
- \( A = 29160 \)
- \( R = 8 \)
- \( D = 2 \)

### Step 1: Substitute the known values into the formula
\[ 29160 = P \left(1 + \frac{8}{100}\right)^2 \]

### Step 2: Simplify the expression inside the parentheses
\[ 1 + \frac{8}{100} = 1 + 0.08 = 1.08 \]

### Step 3: Calculate \( (1.08)^2 \)
\[ (1.08)^2 = 1.1664 \]

### Step 4: Substitute this back into the equation
\[ 29160 = P \times 1.1664 \]

### Step 5: Solve for \( P \)
To find \( P \), divide both sides by 1.1664:
\[ P = \frac{29160}{1.1664} \]

### Step 6: Perform the division
Calculating this gives:
\[ P = 25000 \]

Thus, the sum of money which will become Rs 29,160 at the rate of 8% per annum compound interest in two years is **Rs 25,000**.