Krishna borrows Rs. 45K from a bank at 10% compound interest. He repays it in…

Step-by-Step Solution

To find the first installment, we need to set up the equation for the present value of the installments, which must equal the loan amount of Rs. 45,000.

1. Define the installments:

   • The three annual installments are in arithmetic progression. Let them be:

     • Installment 1 (Year 1): a - d

     • Installment 2 (Year 2): a

     • Installment 3 (Year 3): a + d

   • Total paid = (a - d) + a + (a + d) = 3a = 54,000

   • Therefore, a = 18,000.

   • The installments are: (18,000 - d), 18,000, and (18,000 + d).

2. Set up the present value equation:

   • With 10% compound interest, the present value (PV) of the installments must equal the loan amount (Rs. 45,000).

   • PV = (18,000 - d) / 1.1 + 18,000 / 1.1^2 + (18,000 + d) / 1.1^3 = 45,000

   • 1.1^3 is 1.331. Multiplying the entire equation by 1.331 to clear the denominators:

   • 1.21 * (18,000 - d) + 1.1 * 18,000 + (18,000 + d) = 45,000 * 1.331

   • 21,780 - 1.21d + 19,800 + 18,000 + d = 59,895

   • 59,580 - 0.21d = 59,895

   • 0.21d = -315

   • d = -1,500.

3. Calculate Year 1 payment:

   • Year 1 installment = a - d

   • Year 1 = 18,000 - (-1,500) = 19,500.