IE343_HW3_Solutions

# IE343_HW3_Solutions - Homework Assignment #3 Solutions...

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Unformatted text preview: Homework Assignment #3 Solutions PURDUE UNIVERSITY IE 343: Engineering Economics Fall 2010 Instructor: A. Capponi Homework Assignment #3 Assigned: 10 Sept 2010 Due: 17 Sept 2010 Missing name on the top of each page submitted – 2 Not stapled together – 2 In the future, if the homework is not completed on the correct template you will receive – 10 Problem 1 Textbook Problem 4-41 (5 points) Show (A/P, i, N) = i / [1-(P/F, i, N)]. ( ( [( ( ) ) ) ( ( ) ) ) ( ( [( ) ) ) * [ ( ( ( ) ) )+ Problem 2 (5 points) Textbook Problem 4-50 (Use Excel functions) You must use an Excel function. To receive credit, you must write out the excel equation you use. Example: Answer = FUNCTION(variable, variable, etc.) Present Value = -1,000,000 Annuity = 100,000 Interest = 6% Years until depleted = 15.7 years =NPER(6%, 100000,-1000000) Interest = 8% Years until depleted = 20.9 years =NPER(8%, 100000,-1000000) IE 343 – Homework Assignment #3 Solutions – Page 1 Homework Assignment #3 Solutions Problem 3 Textbook Problem 4-54 (5 points) The loan after 12 months ( ) The end-of-month payment ( ) Problem 4 Textbook Problem 4-72 (15 points) How many years must the system last? N=? Equivalent cash inflows = Equivalent cash outflows Using time 0 as the equivalence point N = total life of the system ( ) ( ) ( ( ) ( ) )( ( ) ) ) ( ( (P/A,18%,N−2) = 4.297 From Table C-16, (P/A, 18%, 8) = 4.0776 and (P/A,18%,9) = 4.3030 Thus, (N−2) = 9 and N = 11 years. At least, it should last for 11 years. IE 343 – Homework Assignment #3 Solutions – Page 2 )( ) Homework Assignment #3 Solutions Problem 5 Textbook Problem 4-74 (15 points) The uniform annual amount is given by the sum of the annuity of the uniform series and the annuity equivalent to an Arithmetic Gradient Series, where G = \$100, the interest rate per period (per year) is 8%, and the number of periods is N = 20 years. We obtain A2 = A1 + G (A/G,i%,N) A2 = 500 + 100(A/G,8%,20) A2 = 500 + 100(7.036948) A2 = 500 + 703.69 = \$1203.69 Problem 6 Textbook Problem 4-75 (15 points) The present value of the investment is ( ) ( ) The future value of the investment is ( ) ( )( ) ( Using either the Present or Future Values, it seems like a good investment. IE 343 – Homework Assignment #3 Solutions – Page 3 ) Homework Assignment #3 Solutions Problem 7 Suppose you get a mortgage loan of \$50,000 to be repaid in 30 years. (15 points) a) Using the mortgage calculator spreadsheet available on VISTA, produce a graph which displays, for each month, the amount of repaid principal (also called normal paydown) and the interest paid when the nominal mortgage rate is r = 5.33% compounded monthly. (You may want to understand the spreadsheet first). Please, don’t just report the graph, but also explain how you modified the formulas in the spreadsheet. We only need to set the interest rate r = 5:33% in the mortgage calculator spreadsheet, and the loan amount to \$55,000. We obtain the graph below. (Please see also the spreadsheet for more details) Paydown vs Interest \$300.00 \$250.00 Normal Paydown Interest Payment \$200.00 \$150.00 \$100.00 \$50.00 \$0.00 1 47 93 139 185 231 Month 277 323 IE 343 – Homework Assignment #3 Solutions – Page 4 Homework Assignment #3 Solutions b) Suppose now that the loan is repaid on a quarterly basis. Add a new sheet to the Excel file, and produce a graph which displays, for each quarter, the amount of repaid principal and the interest paid when the nominal mortgage rate is r = 5.33% compounded quarterly. Please, do not just report the graph, but also report the Excel formulas you used. Since the interest rate is compounded quarterly, we need to divide the nominal rate r by 4, which is going to give us the interest rate per quarter. Using this rate to compute the annuity payment, and the interest on the remaining principal, we obtain the following graph Paydown vs Interest \$900.00 \$800.00 \$700.00 Payment \$600.00 \$500.00 Normal Paydown \$400.00 Interest \$300.00 \$200.00 \$100.00 \$0.00 1 47 93 Quarters c) Briefly, comment on the results you obtain. From both graphs, we can see that, in the beginning, most of the annuity payment is used to repay the interest on the principal (loan). As the amount of principal due decreases, most of the annuity payment is used to repay the remaining principal due. IE 343 – Homework Assignment #3 Solutions – Page 5 ...
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## This note was uploaded on 09/19/2011 for the course IE 343 taught by Professor Vincent,g during the Spring '08 term at Purdue.

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