Mathematics for FinanceMTP 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 a — 2,000\displaystyle 2,000

All Options:

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

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.

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