Mathematics for FinancePYQ June 22Question 1455 of 512
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Anshika took a loan of ₹1,00,000\displaystyle ₹ 1,00,000 @ 8%\displaystyle 8\% for 5\displaystyle 5 years. What amount will she pay if she wants to pay the whole amount in five equal installments?

Options

A₹25,045.63\displaystyle ₹ 25,045.63
B₹26,045.68\displaystyle ₹ 26,045.68
C₹28,045.50\displaystyle ₹ 28,045.50
DNone of these
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Correct Answer

✅ Option a — ₹25,045.63\displaystyle ₹ 25,045.63

All Options:

  • A₹25,045.63\displaystyle ₹ 25,045.63
  • B₹26,045.68\displaystyle ₹ 26,045.68
  • C₹28,045.50\displaystyle ₹ 28,045.50
  • DNone of these

Detailed Solution & Explanation

Let the equal annual installment be A\displaystyle A. Given parameters: * Loan Amount (PV\displaystyle PV) = Rs. 1,00,000\displaystyle \text{Rs. }1,00,000 * Time (n\displaystyle n) = 5\displaystyle 5 years * Interest Rate (r\displaystyle r) = 8%\displaystyle 8\% p.a. compounded annually, so i=0.08\displaystyle i = 0.08 The formula for the Present Value of an ordinary annuity is: PV=A×1−(1+i)−niPV = A \times \frac{1 - (1+i)^{-n}}{i} Substituting the values: 1,00,000=A×1−(1.08)−50.081,00,000 = A \times \frac{1 - (1.08)^{-5}}{0.08} First, let's calculate (1.08)−5\displaystyle (1.08)^{-5}: (1.08)−5≈0.680583(1.08)^{-5} \approx 0.680583 Now substitute this back: 1,00,000=A×1−0.6805830.081,00,000 = A \times \frac{1 - 0.680583}{0.08} 1,00,000=A×0.3194170.081,00,000 = A \times \frac{0.319417}{0.08} 1,00,000=3.99271A1,00,000 = 3.99271 A Solving for A\displaystyle A: A=1,00,0003.99271≈25,045.63A = \frac{1,00,000}{3.99271} \approx 25,045.63 Thus, the annual installment is approximately Rs. 25,045.63\displaystyle \text{Rs. }25,045.63. Hence, **Option A** is the correct answer.

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