The Russell Index tracks the average performance of various groups of stocks. Figure 3 shows that, on average, a $ 10 , 000 investment in midcap growth funds over a 10 -year period would have grown to $ 63 , 000 . What annual nominal rate would produce the same growth if interest were (A) compounded annually? (B) compounded continuously? Express answers as percentages, rounded to three decimal places.
The Russell Index tracks the average performance of various groups of stocks. Figure 3 shows that, on average, a $ 10 , 000 investment in midcap growth funds over a 10 -year period would have grown to $ 63 , 000 . What annual nominal rate would produce the same growth if interest were (A) compounded annually? (B) compounded continuously? Express answers as percentages, rounded to three decimal places.
Solution Summary: The author calculates the annual nominal rate compounded annually when 10000 is invested for 10 years. The formula for compound interest is represented by A=P(1+rright
The Russell Index tracks the average performance of various groups of stocks. Figure
3
shows that, on average, a
$
10
,
000
investment in midcap growth funds over a
10
-year period would have grown to
$
63
,
000
. What annual nominal rate would produce the same growth if interest were
(A) compounded annually?
(B) compounded continuously?
Express answers as percentages, rounded to three decimal places.
59. At a certain gas station, 40% of the customers use regular gas (A1), 35% use plus gas (A2), and 25% use premium (A3). Of those customers using regular gas, only 30% fill their tanks (event B). Of those customers using plus, 60% fill their tanks, whereas of those using premium, 50% fill their tanks.a. What is the probability that the next customer will request plus gas and fill the tank (A2 B)?b. What is the probability that the next customer fills the tank?c. If the next customer fills the tank, what is the probability that regular gas is requested? Plus? Premium?
38. Possible values of X, the number of components in a system submitted for repair that must be replaced, are 1, 2, 3, and 4 with corresponding probabilities .15, .35, .35, and .15, respectively.
a. Calculate E(X) and then E(5 - X).b. Would the repair facility be better off charging a flat fee of $75 or else the amount $[150/(5 - X)]?
[Note: It is not generally true that E(c/Y) = c/E(Y).]
74. The proportions of blood phenotypes in the U.S. popula- tion are as follows:A B AB O
.40 .11 .04 .45
Assuming that the phenotypes of two randomly selected individuals are independent of one another, what is the probability that both phenotypes are O? What is the probability that the phenotypes of two randomly selected individuals match?
Chapter 3 Solutions
Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
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