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

A trust will receive Rs 3,000 at the end of each year forever, with the first receipt at the end of year 3. If the interest rate is 25% p.a., what is the present value today? (Use 1.25^2 = 1.5625)

The present value is Rs 7,680. The perpetuity is worth 3,000 divided by 0.25, which is Rs 12,000, as at the end of year 2, one period before the first payment. Discounting that for two years at 25% gives 12,000 divided by 1.5625, which is 7,680.

  1. ARs 7,680Correct
  2. BRs 9,600
  3. CRs 6,144
  4. DRs 12,000

Explanation

At the end of year 2, the perpetuity is worth 3,000/0.25 = Rs 12,000, since the first payment is one year later. Discount this two years: 12,000/1.5625 = Rs 7,680. Rs 9,600 discounts only one year. Rs 6,144 discounts three years (12,000/1.953125). Rs 12,000 does not discount at all.

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