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Department of Mathematical Sciences
Math 131 Second Major Exam
Wednesday August 4, 2004 Semester III, 2003-2004 (033)
Name _______________________________________ ID # _________________ Section #________
Determine the interest rate r which is compounded continuously to give an effective rate of 9%.
(2 points)
A trust fund is to be established by a single payment so that at the end of 15 years, there will be $20,000 in the fund. If the fund earns interest at the rate of 8% compounded semiannually, how much should be deposited initially into the fund? (2 points)
Suppose you deposit a monthly payment at the beginning of every month into a bank account that pays 6% compounded monthly. If after six years you will have $17,368.18, how much is the monthly payment? (3 points)
A debt of $2000 due in one year is to be repaid by a payment due two years from now and a final payment of $1000 three years from now. If the interest is at the rate of 4% compounded annually, what is the payment due in two years? (3 points)
Given an interest rate of 7.25% compounded monthly, find the present value of the following annuity: $700 at the end of each month for three years and $900 at the end of each month for five more years. (4 points)
A company will hire five people: three for the assembly department and two for the finishing department. There are eight applicants who are equally qualified to work in each department. In how many ways can the company fill the positions? (2 points)
Five different books are to be arranged horizontally on a bookshelf. (2 points)
In how many ways can this be done?
If two are mathematics books and three are accounting books, in how many ways can all the books be arranged if the first two books are to be in mathematics?
If P(E) = 0.4, P( EMBED Equation.DSMT4 ) = 0.6, and P( EMBED Equation.DSMT4 ) = 0.1, find P(F'). (2 points)
Three fair coins are tossed. Find the probability that (2 points)
three tails show
exactly two tails show.
A university is considering a specific action. An opinion survey of 200 people was conducted and the results are indicated in the following table: (3 points)
FavorOpposeNo OpinionTotalFaculty4035984Student6030696Staff48820Total1047323200If a person is selected at random, determine each of the following (empirical) probabilities:
P (opposes the action)
P (faculty who favors the action)
P (student or has no opinion).
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