A loan of at per annum compound interest (compounded annually) is repaid in two equal annual installments, the first paid at the end of year and the second at the end of year . What is the amount of each installment?
Answer and explanation
Correct answer: A.
- Step 1: Let denote each equal annual installment. At annual compound interest, the present value of the two payments must equal the principal of ₹.
- Step 2: Set up the present value equation: , which simplifies to .
- Step 3: Solve for : .
Answer
.
Why not the others: ₹ divides principal by 2 with zero interest; ₹ calculates simple interest for one year and divides by 2; ₹ applies two years of simple interest; ₹ computes compound amount over two years and divides by 2.
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