An employee had the following percentage increases in salary over the last 5 years: 4%, 7%, 10%, 15%, 12%.The geometric mean of his salary increases equals ________.
Answer(s): D
The straight geometric mean of the increases is (0.04*0.07*0.1*0.15*0.12)^(1/5) = 8.72%. Note that this is different from geometric rate of change, which in this case would be (1.04*1.07*1.1*1.15*1.12)^(1/5) - 1 = 9.53%. You should be very careful about this point since the Mason & Lind textbook is quite ambiguous on this point. Finally, note that the geometric mean may not be defined if some of the salary changes are negative.
Suppose that stocks A, B, C, and D are independent with respect to their price movement, and have probabilities of increasing of 0.25, 0.50, 0.40, and 0.30. What is the probability that stocks A and C will increase in price? In other words, find P(AC).
Answer(s): C
If events are independent, then the joint probability of them occurring together is just the product of the individual probabilities. So P(AC) = 0.25 * 0.40 = 10%. Note that we did not state whether the other stocks, B and D, increased in value or not.
A stock has the following returns over 3 years: +2%, +15%, +25%. The annual geometric rate of return over the three years is ________.
Answer(s): H
The annual geometric rate of return equals [(1+2%)(1+15%)(1+25%)]^(1/3) - 1 = (1.02 * 1.15 * 1.25)^0.33 - 1 = 0.1361 = 13.61%
What annual interest rate, compounded annually, would cause a series of 30 deposits of $500 to accumulate to $50,000, if the first deposit is made one year from today?
On the BAII Plus, press 30 N, 0 PV, 500 PMT, 50000 +/- FV, CPT I/Y. On the HP12C, press 30 n, 0 PV, 500 PMT, 50000 CHS FV, i. Make sure the BAII Plus has the P/Y value set to 1.
A true-false test consists of six questions. If you guess the answer to each question, what is the probability of getting all six questions correct?
Answer(s): E
This is binomial distribution with p = 0.5, q = 0.5, n = 6, r = 6. Therefore 6!(0.5^6)(0.5^0)/6!0! = 0.0156.
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