Mathematics of FinanceMCQPYQ 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

A25,045.63\displaystyle ₹ 25,045.63
B26,045.68\displaystyle ₹ 26,045.68
C28,045.50\displaystyle ₹ 28,045.50
DNone of these
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Correct Answer

Option a25,045.63\displaystyle ₹ 25,045.63

All Options:

  • A25,045.63\displaystyle ₹ 25,045.63
  • B26,045.68\displaystyle ₹ 26,045.68
  • C28,045.50\displaystyle ₹ 28,045.50
  • DNone of these

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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)50.680583(1.08)^{-5} \approx 0.680583 Now substitute this back: 1,00,000=A×10.6805830.081,00,000 = 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=1,00,0003.9927125,045.63A = \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.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

Weightage

12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

View Official ICAI Syllabus

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