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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Time Value of Money and Annuity - Simple and Compound Interest

A scholarship fund pays Rs 4,500 at the end of every year forever. If the fund earns 9% p.a., what sum must be invested today to meet this payment indefinitely?

The sum required is Rs 50,000. For a perpetuity paid at the end of each year, the present value equals the annual payment divided by the interest rate, so 4,500 divided by 0.09 gives Rs 50,000, which earns exactly Rs 4,500 annually.

  1. ARs 40,500
  2. BRs 50,000Correct
  3. CRs 45,000
  4. DRs 55,000

Explanation

Present value of a perpetuity = payment / rate = 4,500 / 0.09 = Rs 50,000. Check: 50,000 x 9% = 4,500. Rs 40,500 results from multiplying 4,500 by 9 instead of dividing by 0.09... actually multiplying by 0.09 gives 405, so 40,500 is a wrong-scale error.

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