A sum of `Rs. 210` was taken as a loan. This is to be paid back in two equal instalments. If the rate of interest be `10%` compounded annually, then the value of each instalment is

Options

A. `Rs. 127 `
B. `Rs. 121`
C. `Rs. 210`
D. `Rs. 225 `

Answer

To solve the problem of finding the value of each installment for a loan of Rs. 210 at a 10% compounded interest rate, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Loan and Installments**:
- The total loan amount (Principal) = Rs. 210.
- The loan is to be paid back in two equal installments.
- The rate of interest (R) = 10% per annum.

2. **Calculate the Future Value of Each Installment**:
- Let the value of each installment be \( P \).
- The first installment will be paid at the end of the first year, and the second installment will be paid at the end of the second year.
- The first installment will accrue interest for 1 year, and the second installment will accrue interest for 0 years (since it is paid at the end of the second year).

3. **Set Up the Equation**:
- The future value of the first installment after 1 year = \( P \times (1 + \frac{R}{100}) = P \times 1.1 \).
- The future value of the second installment after 0 years = \( P \).
- The total amount to be paid back after 2 years = Future value of first installment + Future value of second installment.
- Therefore, we can write the equation:
\[ P \times 1.1 + P = 210 \]

4. **Combine Like Terms**:
- Combine the terms on the left side:
\[ 1.1P + P = 210 \]
\[ 2.1P = 210 \]

5. **Solve for P**:
- Divide both sides by 2.1 to find the value of each installment:
\[ P = \frac{210}{2.1} \]
\[ P = 100 \]

6. **Conclusion**:
- Each installment is Rs. 100.

### Final Answer:
The value of each installment is **Rs. 100**.