Mathematics of FinanceMCQMTP Nov 19Question 1505 of 512
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An asset of 50,000\displaystyle 50,000 to be paid back in equal annual installments over a period of 20\displaystyle 20 years. Find the value of installment, if interest is compounded annually at 14%\displaystyle 14\% per annum. [Given (1.14)20=13.74349]\displaystyle [Given \ (1.14)^{20} = 13.74349]

Options

A550.50\displaystyle 550.50
B549.30\displaystyle 549.30
C559.50\displaystyle 559.50
D560.50\displaystyle 560.50
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Correct Answer

Option a550.50\displaystyle 550.50

All Options:

  • A550.50\displaystyle 550.50
  • B549.30\displaystyle 549.30
  • C559.50\displaystyle 559.50
  • D560.50\displaystyle 560.50

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Detailed Solution & Explanation

The loan instalment (A\displaystyle A) required to pay back an asset value of PV\displaystyle PV over n\displaystyle n years at interest rate i\displaystyle i is: A=PVP(n,i)A = \frac{PV}{P(n, i)} Given: * Asset value (PV\displaystyle PV) = 50,000\displaystyle 50,000 * Time (n\displaystyle n) = 20\displaystyle 20 years * Interest rate (i\displaystyle i) = 14%\displaystyle 14\% p.a. = 0.14\displaystyle 0.14 * Annuity factor P(20,0.14)=1(1.14)200.14=6.62313\displaystyle P(20, 0.14) = \frac{1 - (1.14)^{-20}}{0.14} = 6.62313 Substituting the values: A=50,0006.623137,549.30A = \frac{50,000}{6.62313} \approx 7,549.30 The options provided in the question are around 550\displaystyle 550 (e.g., 550.50\displaystyle 550.50), indicating a potential typo in the asset amount in the source paper (e.g., if it was 3,640\displaystyle 3,640, then A549.58\displaystyle A \approx 549.58). Based on the official key: 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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