A man borrows Rs. 21000 at 10% compound interest. How much he has to pay equally at the end of each year, to settle his loan in two years?

Answer

To solve the problem of how much the man has to pay equally at the end of each year to settle his loan in two years, we can follow these steps:

### Step 1: Understand the Loan Amount and Interest Rate
The man borrows Rs. 21,000 at a compound interest rate of 10% per annum.

### Step 2: Calculate the Total Amount Payable at the End of Each Year
Since the loan is to be settled in two years, we need to calculate the total amount payable at the end of each year, considering the compound interest.

1. **First Year:**
- Amount at the end of the first year = Principal + Interest
- Interest for the first year = Principal × Rate = 21000 × 10% = 2100
- Total amount after the first year = 21000 + 2100 = Rs. 23100

2. **Second Year:**
- Now, the principal for the second year is Rs. 23100.
- Interest for the second year = 23100 × 10% = 2310
- Total amount after the second year = 23100 + 2310 = Rs. 25410

### Step 3: Set Up the Equation for Equal Installments
Let the equal installment amount be Rs. X. Since he pays this amount at the end of each year, we can express the total amount paid as:
- Amount paid after 1st year = X
- Amount paid after 2nd year = X

The present value of these payments must equal the total amount payable at the end of the loan period, which is Rs. 25410.

Using the formula for present value of the installments:
\[ X + \frac{X}{(1 + r)} = 25410 \]
Where \( r = 10\% = 0.10 \).

### Step 4: Solve the Equation
Substituting the value of r:
\[ X + \frac{X}{1.1} = 25410 \]

To solve this, we can multiply through by 1.1 to eliminate the fraction:
\[ 1.1X + X = 25410 \times 1.1 \]
\[ 2.1X = 27951 \]

Now, divide both sides by 2.1:
\[ X = \frac{27951}{2.1} \]
\[ X = 13300 \]

### Conclusion
Thus, the man has to pay Rs. 13,300 at the end of each year to settle his loan in two years.

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