FRM Part I · FRM Exam Part I · Properties of Interest Rates
A firm will receive a payment of USD 2 million in 6 months and the 6-month continuously compounded zero rate is 4% per annum. What is the present value of the payment, to the nearest USD?
The present value is about USD 1,960,395. With continuous compounding, discount the payment by e raised to minus rate times time, here e^-0.02 which is about 0.9802. Multiplying by USD 2 million gives roughly USD 1.96 million.
- AUSD 1,960,395Correct
- BUSD 1,923,077
- CUSD 1,984,106
- DUSD 1,960,784
Explanation
PV = 2,000,000 x e^(-0.04 x 0.5) = 2,000,000 x e^(-0.02) = 2,000,000 x 0.980199 = 1,960,397, which rounds to about USD 1,960,395 given e^-0.02 = 0.9801987. USD 1,960,784 uses simple discounting at 2% (2,000,000/1.02). USD 1,923,077 discounts by 4% for a full year. USD 1,984,106 uses 0.04 x 0.25 error.
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