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Unformatted text preview: Name: Tuesday, September 21 st ACF329/M389F Theory of Interest Fall 2010 University of Texas at Austin InTerm 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 singleword 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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 Spring '08
 Maxwell

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