Compute the present discounted value of the following income streams. Assume the

Question

Compute the present discounted value of the following income streams. Assume the interest rate is 50,000, received 1 year from now. $50,000, received 10 years from now. $100 every year, forever, starting immediately. $100 every year, forever, starting 1 year from now. $100 every year for the next 50 years, starting immediately. Repeat exercise 4 for an interest rate of 1%, then for an interest rate of 5%. Arrange your answers in a table so you can more easily see the difference a change in the interest rate makes.How many leaves does a 4-ary tree have if its depth is 6? How many total nodes does a 6-ary tree have if its depth is 5? Given the preorder traversal of a tree is: a.b.c.d.e and the inoder traversal of the tree is: b,a,e,d,c. What is the POSTORDER traversal of that tree? Evaluate performance characteristics (list the total number of comparisons and which character positions in the string to the LEFT of the match were not used in a comparison) of three string matching algorithms for the following case:Brute Force Knuth-Morris-Pratt Boyer-Moore Hash the given file (6,22.9.14,13,1,8,34) and use linear probing and the table size of 11. How many total collisions occurred? What is the loading density of the table? How many comparisons are needed to determine whether key value 12 is in the table? Using the same list of values and hash table size as in problem 5. but overflow chaining What is the longest overflow chain? What is the loading density of the table? How many comparisons are needed to determine whether key value 12 is in the table?What should the loading factor be (on ANY HASH TABLE) if you want to have an average of 1.4 comparisons per search if LINEAR PROBING? Thinking back to the method used to represent a full, left-justified tree in an array used by heapsort. how would you define the following for a full, left-justified 3 - ary tree (use subscripts 1,2,..., n for your array). As a reminder, for a binary tree, we use the following: Parent |_i/2j Left 2 middot i Right 2 middot i + 1

Explanation / Answer

Present Value of Perpetuity starting immediately = Cash flow / Interest rate = 100 / 0.03 = $3333.33

Present Value of Perpetuity starting immediately = Cash flow / Interest rate = 100 / 0.01 = $10000

Present Value of Perpetuity starting immediately = Cash flow / Interest rate = 100 / 0.05 = $2000

Present Value of Perpetuity starting after 1 year = 97.09 / 0.03 = $3236.33

Present Value of Perpetuity starting after 1 year = 99.01 / 0.01 = $9901

Present Value of Perpetuity starting after 1 year = 95.24 / 0.05 = $1904.80

Year Cashflow Interest Present Value 1 50000 3% 48543.69 1 50000 1% 49504.95 1 50000 5% 47619.05 Year Cashflow Interest Present Value 10 50000 3% 37204.70 10 50000 1% 45264.35 10 50000 5% 30695.66 Year Cashflow Interest Present Value 1 100 3% 97.09 1 100 1% 99.01 1 100 5% 95.24

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