Mathematics of FinanceMCQMTP May 20, ICAI SMQuestion 1568 of 512
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A person desires to create a fund to be invested at 10%\displaystyle 10\% CI per annum to provide for a prize of 300\displaystyle 300 every year. Using V=a/i\displaystyle V = a/i find V\displaystyle V and V\displaystyle V will be

Options

A2,000\displaystyle 2,000
B2,500\displaystyle 2,500
C3,000\displaystyle 3,000
DNone of these
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Correct Answer

Option a2,000\displaystyle 2,000

All Options:

  • A2,000\displaystyle 2,000
  • B2,500\displaystyle 2,500
  • C3,000\displaystyle 3,000
  • DNone of these

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Detailed Solution & Explanation

The present value (V\displaystyle V) of the perpetuity fund to provide a perpetual annual prize is: V=aiV = \frac{a}{i} Given: * Annual prize amount (a\displaystyle a) = 300\displaystyle 300 * Interest rate (i\displaystyle i) = 10%\displaystyle 10\% p.a. = 0.10\displaystyle 0.10 Substituting the values: V=3000.10=3,000V = \frac{300}{0.10} = 3,000 Mathematically, the required fund is 3,000\displaystyle 3,000 (Option C). However, the official key marks Option A (2,000\displaystyle 2,000). 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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