Rs 15000 becomes Rs 16100 in 4 years at the rate of 10% interest per annum. If this sum is returned in 4 equal yearly installments. Then find the installment.

Options

A. Rs 3500
B. Rs 3600
C. Rs 3800
D. Rs 3400

Answer

To solve the problem of finding the equal yearly installment for a sum of Rs 15,000 that becomes Rs 16,100 in 4 years at a rate of 10% interest per annum, we can follow these steps:

### Step 1: Understand the Total Amount and Interest
The principal amount (P) is Rs 15,000, and it grows to Rs 16,100 after 4 years. The total interest earned over 4 years can be calculated as:
\[ \text{Total Interest} = \text{Final Amount} - \text{Principal} = 16,100 - 15,000 = 1,100 \]

**Hint:** Calculate the total interest earned by subtracting the principal from the final amount.

### Step 2: Calculate the Total Amount in Terms of Installments
We need to return the total amount of Rs 16,100 in 4 equal yearly installments. Let the installment amount be \( x \).

### Step 3: Consider the Effect of Interest on Each Installment
Each installment will accrue interest for the remaining years until the total is paid off. The first installment will not accrue interest, the second will accrue interest for 1 year, the third for 2 years, and the fourth for 3 years.

1. First installment (no interest): \( x \)
2. Second installment (1 year interest): \( x \times (1 + 0.10) = 1.1x \)
3. Third installment (2 years interest): \( x \times (1 + 0.10)^2 = 1.21x \)
4. Fourth installment (3 years interest): \( x \times (1 + 0.10)^3 = 1.331x \)

### Step 4: Set Up the Equation
The total amount paid back after 4 years is:
\[ x + 1.1x + 1.21x + 1.331x = 16,100 \]

Combine the terms:
\[ (1 + 1.1 + 1.21 + 1.331)x = 16,100 \]
Calculating the sum:
\[ 1 + 1.1 + 1.21 + 1.331 = 4.641 \]
Thus, we have:
\[ 4.641x = 16,100 \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides by 4.641:
\[ x = \frac{16,100}{4.641} \approx 3,469.72 \]

### Conclusion
The equal yearly installment is approximately Rs 3,469.72.

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