A loan was repaid in two annual instalments of Rs 121 each . if rate of interest be `10%` per annum. Compounded annually the sum borrowed was-

Options

A. Rs.200
B. Rs.210
C. Rs.217.80
D. Rs.280

Answer

To find the sum borrowed when a loan is repaid in two annual installments of Rs 121 each at a rate of interest of 10% compounded annually, we can follow these steps:

### Step 1: Understand the Problem
We have two installments of Rs 121 each. The interest rate is 10% per annum, compounded annually. We need to find the principal amount (sum borrowed).

### Step 2: Set Up the Formula
The present value (PV) of the installments can be calculated using the formula for present value of an annuity:
\[ PV = \frac{C}{(1 + r)^1} + \frac{C}{(1 + r)^2} \]
Where:
- \(C\) = annual installment (Rs 121)
- \(r\) = rate of interest (10% or 0.10)

### Step 3: Substitute the Values
Substituting the values into the formula:
\[ PV = \frac{121}{(1 + 0.10)^1} + \frac{121}{(1 + 0.10)^2} \]
This simplifies to:
\[ PV = \frac{121}{1.10} + \frac{121}{1.10^2} \]

### Step 4: Calculate Each Term
Calculate the first term:
\[ \frac{121}{1.10} = \frac{121}{1.10} = 110 \]
Calculate the second term:
\[ \frac{121}{1.10^2} = \frac{121}{1.21} = 100 \]

### Step 5: Add the Present Values
Now, add the present values of both installments:
\[ PV = 110 + 100 = 210 \]

### Conclusion
The sum borrowed (the principal amount) is Rs 210.