ENGINEERING ECONOMY DIGITAL ACCESS
ENGINEERING ECONOMY DIGITAL ACCESS
8th Edition
ISBN: 2810022611683
Author: Blank
Publisher: MCG
Question
Book Icon
Chapter 3, Problem 54P
To determine

Calculate the time period.

Expert Solution & Answer
Check Mark

Explanation of Solution

The present value (P) is $20,000. The first withdraw (D) is $5,000 that has taken place now. The second year’s withdrawal (D2) is $4,500 and decreases the withdrawal (d) by $500. Thereafter, interest rate (i) is 8%.

Time period (n) can be calculated as follows:

P=W+W2((1+i)n1i(1+i)n)d×1i((1+i)n1i(1+i)nn(1+i)n)20,000=5,000+4,500((1+0.08)n10.08(1+0.08)n)500×10.08((1+0.08)n10.08(1+0.08)nn(1+0.08)n)20,0005,000=4,500((1+0.08)n10.08(1+0.08)n)500×12.5((1+0.08)n10.08(1+0.08)nn(1+0.08)n)15,000=4,500((1+0.08)n10.08(1+0.08)n)500×12.5((1+0.08)n10.08(1+0.08)nn(1+0.08)n)

Substitute the time period as 5 years in the above calculation.

15,000=4,500((1+0.08)510.08(1+0.08)5)500×12.5((1+0.08)510.08(1+0.08)55(1+0.08)5)15,000=4,500(1.469310.08(1.4693))500×12.5(1.469310.08(1.4693)51.4693)15,000=4,500(0.46930.1175)500×12.5(0.46930.11753.403)15,000=4,500(3.994)500×12.5(3.9943.403)15,000=17,9733,693.7515,000>14,279.25

The calculated value is less than $15,000. Thus, it increases the time period to 5.6.

15,000=4,5000((1+0.08)5.610.08(1+0.08)5.6)500×12.5((1+0.08)5.610.08(1+0.08)5.65.6(1+0.08)5.6)15,000=4,500(1.538810.08(1.5388))500×12.5(1.538810.08(1.5388)5.61.5388)15,000=4,500(0.53880.1231)500×12.5(0.53880.12313.6392)15,000=4,500(4.3769)500×12.5(4.37693.6392)15,000=19,696.05500×12.5(0.7377)15,000=19,696.054,610.62515,00015,085.43

Since the calculated value is nearly equal to $15,000, it is confirmed that the time period is 5.6 years.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Please answer questions D-H, I have already answered A , B,C but it may help you to still solve them yourself. Thank you!
2. A firm’s production function is given by:Q = 10KLThe unit capital and labour costs are 2 and 1 pounds respectively. The firm is contracted to produce2000 units.(a) Write out the optimisation problem of the firm. (b) Express this problem using a Lagrangian function. (c) Find values of K and L which fulfil the contract with minimal cost to the firm. (d) Calculate the total cost to the firm.
3. Consider the following estimated regression equation, estimated using a sample of firms, where RDis total firm spending on research and development in USD ($), Revenue is total firm revenuein USD ($), and W ages is the firms’ total spending on wages in USD ($) (standard errors inparentheses):RDd = 1000(600)+ 0.5(0.1)Revenue + 1.5(0.5)W ages,(a) Interpret the coefficients on each of the explanatory variables. (b) Which of the three coefficients are statistically significant at the 5% level of significance? Howdo you know? A researcher runs a two-sided statistical test of the null hypothesis that both the coefficients onthe explanatory variables above are jointly equal to 0.25 (mathematically, that β1 = β2 = 0.25),and reports a p-value of 0.045.(c) What does this p-value mean for the outcome of the test? (d) What would an appropriate two-sided alternative hypothesis look like?
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
ENGR.ECONOMIC ANALYSIS
Economics
ISBN:9780190931919
Author:NEWNAN
Publisher:Oxford University Press
Text book image
Principles of Economics (12th Edition)
Economics
ISBN:9780134078779
Author:Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:PEARSON
Text book image
Engineering Economy (17th Edition)
Economics
ISBN:9780134870069
Author:William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:PEARSON
Text book image
Principles of Economics (MindTap Course List)
Economics
ISBN:9781305585126
Author:N. Gregory Mankiw
Publisher:Cengage Learning
Text book image
Managerial Economics: A Problem Solving Approach
Economics
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Cengage Learning
Text book image
Managerial Economics & Business Strategy (Mcgraw-...
Economics
ISBN:9781259290619
Author:Michael Baye, Jeff Prince
Publisher:McGraw-Hill Education