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

Mr. Reddy will receive Rs 2,000 at the end of each year for 3 years and, on the same terms, a perpetuity of Rs 2,000 a year would start at the end of year 4 and continue forever. At 10% per annum, what is the present value today of this entire stream (all payments from year 1 onwards, Rs 2,000 each year forever)? Use (1.10)^3 = 1.331.

The present value is Rs 20,000. Equal payments of Rs 2,000 at every year end forever from year 1 form one ordinary perpetuity, so value equals 2,000 divided by 0.10. Splitting into a three-year annuity and a deferred perpetuity gives the same total.

  1. ARs 22,000
  2. BRs 20,000Correct
  3. CRs 18,000
  4. DRs 24,000

Explanation

Payments of Rs 2,000 at the end of every year forever from year 1 form an ordinary perpetuity: 2,000 / 0.10 = Rs 20,000. Splitting gives the same: 3-year annuity = 2,000 x (1 - 1/1.331)/0.10 = 4,974 approx, plus perpetuity from year 4 = 20,000/1.331 = 15,026, total 20,000. Rs 22,000 wrongly treats it as a perpetuity due.

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