Installment Calculation for Compound Interest Loan

This problem requires calculating the equal installment amount for a loan repaid under compound interest. We need to find the value 'x' for each installment such that the present value of all installments equals the principal amount borrowed.

Loan Details

• Principal Amount (P): ₹2,460
• Annual Interest Rate (R): 5% or 0.05
• Number of Years (n): 2

Installment Calculation Formula

The principal amount (P) is the sum of the present values of each equal installment (x) paid over 'n' years at an interest rate 'R'. For n=2 years, the formula is:

$P = \(\frac{x}{1 + R} + \frac{x}{(1 + R)^2}\)$

Substituting the given values:

$₹2,460 = \(\frac{x}{1 + 0.05} + \frac{x}{(1 + 0.05)^2}\)$

Step-by-Step Calculation

1. Simplify the equation:

   $₹2,460 = \(\frac{x}{1.05} + \frac{x}{(1.05)^2}\)$

   $₹2,460 = \(\frac{x}{1.05} + \frac{x}{1.1025}\)$

2. Factor out 'x':

   $₹2,460 = x \left( \frac{1}{1.05} + \frac{1}{1.1025} \right)$

3. Find a common denominator for the terms inside the parenthesis. Alternatively, use fractions: \(1.05 = \frac{21}{20}\) and \(1.1025 = (\frac{21}{20})^2 = \frac{441}{400}\). Let's recalculate using the decimal common denominator approach for simplicity here. Or better, the fraction approach:

   $₹2,460 = x \left( \frac{20}{21} + \frac{400}{441} \right)$

   $₹2,460 = x \left( \frac{20 \times 21}{441} + \frac{400}{441} \right)$

   $₹2,460 = x \left( \frac{420}{441} + \frac{400}{441} \right)$

   $₹2,460 = x \left( \frac{820}{441} \right)$

4. Solve for 'x':

   $x = ₹2,460 \times \frac{441}{820}$

   $x = \( \frac{2460}{820} \) \times 441$

   $x = 3 \times 441$

   $x = ₹1,323$

Conclusion

Each installment will be ₹1,323.