InTermOneSolutions - Name: Tuesday, September 21 st...

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Unformatted text preview: Name: Tuesday, September 21 st ACF329/M389F Theory of Interest Fall 2010 University of Texas at Austin In-Term Exam I - Solutions Instructor: Milica Cudina Notes : This is a closed book and closed notes exam. The maximal score on this exam is 50 points. Time : 75 minutes TRUE/FALSE 1 (2) TRUE FALSE 2 (2) TRUE FALSE 3 (2) TRUE FALSE 4 (2) TRUE FALSE MULTIPLE CHOICE 1 (3) a b c d e 2 (3) a b c d e FOR GRADERS USE ONLY: T/F 1. 2. 3. 4. 5. 6. 7. M.C. 2 Part I. (8 points) TRUE/FALSE QUESTIONS 1. (2 pts) Let a ( t ) = (1 + 0 . 05) 3 t (1 + 0 . 02) t/ 2 . The force of interest associated with the above accumulation function is constant. Solution: TRUE t = d dt ln( a ( t )) = d dt ln[1 . 05 3 t 1 . 02 t/ 2 ] = 3 ln(1 . 05) + 0 . 5 ln(1 . 02) . 2. (2 pts) In our usual notation, for equivalent d ( n ) and i ( p ) , we have that d ( n ) > i ( p ) . Solution: FALSE See Important fact 1.11.5 in the textbook. 3. (2 pts) Let the amount function A K have the form A K ( t ) = ( t + 1) 3 + ( t + 1) . Then, we know that + = K. Solution: TRUE K = A K (0) = + . 4. (2 pts) If we wish to invest the amount X at a future time t 1 in order to have $S at time t 2 > t 1 , we should invest X = S a ( t 2 ) a ( t 1 ) . Solution: FALSE See Important fact 1.7.4 in the textbook. Part II. Please, explain carefully all your statements and assumptions. Numerical results or single-word answers without an explanation (even if theyre correct) are worth 0 points. 1. (4 points) Source: Problem 1.3.1 from the textbook. You are given that, in our usual notation, A K ( t ) = 1 , 000 100- t t < 100 . (i) (2 pts) Find K . (ii) (2 pts) Find a (20) . Solution: We know that always A K (0) = K . So, in the present problem, K = A K (0) = 1000 100 = 10 ....
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InTermOneSolutions - Name: Tuesday, September 21 st...

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