A sum of ₹ 550 was taken as a loan. This is to be paid back in two equal annual instalments. If the rate of interest be `20%` compounded annually, then the value of each instalments is:

Options

A. 300
B. 360
C. 250
D. none of these

Answer

To find the value of each installment for a loan of ₹550 at an interest rate of 20% compounded annually, we can follow these steps:

### Step 1: Understand the Problem
We need to pay back a loan of ₹550 in two equal annual installments with a compound interest rate of 20%.

### Step 2: Set Up the Equation
Let the value of each installment be \( X \). Since the loan is paid back in two installments, 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.

### Step 3: Calculate the Amount After First Year
After the first year, the loan amount will accrue interest. The amount owed after the first year will be:
\[ \text{Amount after 1 year} = 550 \times (1 + 0.20) = 550 \times 1.20 = 660 \]
After paying the first installment \( X \), the remaining amount will be:
\[ \text{Remaining amount} = 660 - X \]

### Step 4: Calculate the Amount After Second Year
This remaining amount will again accrue interest for one more year:
\[ \text{Amount after 2 years} = (660 - X) \times (1 + 0.20) = (660 - X) \times 1.20 \]
This amount must equal the second installment \( X \):
\[ (660 - X) \times 1.20 = X \]

### Step 5: Solve the Equation
Now, we can expand and solve the equation:
\[ 792 - 1.20X = X \]
Combine like terms:
\[ 792 = X + 1.20X \]
\[ 792 = 2.20X \]
Now, divide both sides by 2.20 to find \( X \):
\[ X = \frac{792}{2.20} = 360 \]

### Conclusion
The value of each installment is ₹360.

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