A borrowed sum was paid in the two annual instalments of ? 121 each . If the rate of compound interest is 10% pa, what sum was borrowed ?

Options

A. X 217.80
B. X 210
C. X 220
D. X 200

Answer

To solve the problem of finding the borrowed sum that was paid in two annual installments of ₹121 each at a compound interest rate of 10% per annum, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Variables**:
- Let the borrowed sum be \( P \).
- The annual installment amount is \( A = 121 \).
- The rate of interest is \( r = 10\% \).

2. **Understanding the Installments**:
- The first installment of ₹121 is paid at the end of the first year.
- The second installment of ₹121 is paid at the end of the second year.

3. **Calculate the Present Value of Each Installment**:
- The present value of the first installment (after 1 year) is calculated using the formula:
\[ PV_1 = \frac{A}{(1 + r/100)^1} = \frac{121}{(1 + 10/100)} = \frac{121}{1.1} \]
- The present value of the second installment (after 2 years) is calculated using the formula:
\[ PV_2 = \frac{A}{(1 + r/100)^2} = \frac{121}{(1 + 10/100)^2} = \frac{121}{(1.1)^2} = \frac{121}{1.21} \]

4. **Calculate Each Present Value**:
- For the first installment:
\[ PV_1 = \frac{121}{1.1} = 110 \]
- For the second installment:
\[ PV_2 = \frac{121}{1.21} \approx 100 \]

5. **Sum of Present Values**:
- The total present value (which equals the borrowed sum \( P \)) is:
\[ P = PV_1 + PV_2 = 110 + 100 = 210 \]

6. **Conclusion**:
- Therefore, the sum that was borrowed is \( P = 210 \) rupees.

### Final Answer:
The borrowed sum is ₹210.