Mohit Anand borrows a certain sum of money from the AMS Bank at 10% per annum at compound interest. The entire debt is discharged in full by Mohit Anand on payment of two equal amounts of 1000 each, one at the end of the first year and the other at the end of the second year. What is the approximate value of the amount borrowed by him?

Options

A. 1852
B. 1736
C. 1694
D. 1792

Answer

To find the approximate value of the amount borrowed by Mohit Anand, we can follow these steps:

### Step 1: Define the principal amount
Let the amount borrowed (principal) be denoted as \( P \).

### Step 2: Calculate the amount after the first year
After one year, the amount owed will be:
\[ A_1 = P \times \left(1 + \frac{R}{100}\right) = P \times \left(1 + \frac{10}{100}\right) = P \times \frac{11}{10} \]
This is the total amount after one year, including interest.

### Step 3: Deduct the first payment
Mohit makes a payment of 1000 at the end of the first year. The remaining amount after this payment will be:
\[ \text{Remaining Amount} = A_1 - 1000 = P \times \frac{11}{10} - 1000 \]

### Step 4: Calculate the amount after the second year
This remaining amount will now accrue interest for another year. The amount after the second year will be:
\[ A_2 = \left(P \times \frac{11}{10} - 1000\right) \times \left(1 + \frac{10}{100}\right) = \left(P \times \frac{11}{10} - 1000\right) \times \frac{11}{10} \]

### Step 5: Set up the equation for the second payment
At the end of the second year, Mohit makes another payment of 1000. Therefore, the total amount owed after the second year should equal this second payment:
\[ A_2 - 1000 = 0 \]
Thus, we have:
\[ \left(P \times \frac{11}{10} - 1000\right) \times \frac{11}{10} - 1000 = 0 \]

### Step 6: Solve for \( P \)
Expanding the equation:
\[ \left(P \times \frac{11}{10} - 1000\right) \times \frac{11}{10} = 1000 \]
\[ P \times \frac{121}{100} - 11000 = 1000 \]
\[ P \times \frac{121}{100} = 11000 + 1000 \]
\[ P \times \frac{121}{100} = 12000 \]
Now, solving for \( P \):
\[ P = \frac{12000 \times 100}{121} \]
\[ P \approx 991.74 \]

### Final Answer
The approximate value of the amount borrowed by Mohit Anand is \( P \approx 991.74 \).

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