Suppose you're an investor who will get interest daily (for an annual rate of, say 5%)...

 

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Suppose you're an investor who will get interest daily (for an annual rate of, say 5%) on $1,000,000. Your interest can be calculated in one of two ways: (a) The sum is calculated every day, and rounded to the nearest cent. This new amount will be used to calculate your sum on the next day. (b) Your sum is calculated only once at the end of the year with the formula Mƒ - Mi(1 + id)d, and then rounded to the = nearest cent. 1. Which method should you choose? How big is the difference? How much smaller is it than the worst-case scenario obtained from mere satisfaction of the IEEE standard? Explain in terms of floating-point error. 2. If the rounding procedure used for the floating-point arithmetic was "round to- ward zero," would you make the same decision? Explain the correspondence between computational error and real-world operations. Suppose you're an investor who will get interest daily (for an annual rate of, say 5%) on $1,000,000. Your interest can be calculated in one of two ways: (a) The sum is calculated every day, and rounded to the nearest cent. This new amount will be used to calculate your sum on the next day. (b) Your sum is calculated only once at the end of the year with the formula Mƒ - Mi(1 + id)d, and then rounded to the = nearest cent. 1. Which method should you choose? How big is the difference? How much smaller is it than the worst-case scenario obtained from mere satisfaction of the IEEE standard? Explain in terms of floating-point error. 2. If the rounding procedure used for the floating-point arithmetic was "round to- ward zero," would you make the same decision? Explain the correspondence between computational error and real-world operations.

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1 You should choose method a where the interest is calculated every day and rounded to the nearest c... View the full answer