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FRM Part I · FRM Exam Part I · Pricing Conventions, Discounting, and Arbitrage

A zero-coupon payment of 1,000 is due in exactly 3 years. The discount rate is 5% per year, compounded annually. What is its present value, to the nearest cent?

The present value is 863.84. Discounting 1,000 over three years at 5% annual compounding means dividing by 1.05 cubed, which is 1.157625. Simple-interest discounting or discounting for only one year gives a different, incorrect value.

  1. A869.57
  2. B863.84Correct
  3. C850.00
  4. D952.38

Explanation

PV = 1,000 / 1.05^3 = 1,000 / 1.157625 = 863.84. The 869.57 option uses simple interest, 1,000 / (1 + 3 x 0.05), which ignores compounding. The 850.00 option subtracts 15% from 1,000. The 952.38 option discounts for only one year.

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