What Are the Present Worth PW and Future Worth FW Engineering Questions

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Topics: • • • • • • • • • • • • • • • • 4.1 Introduction 4.2 Simple Interest 4.3 Compound Interest 4.4 The Concept of Equivalence 4.5 Notation and Cash-Flow Diagrams and Tables 4.6 Relating Present and Future Equivalent Values of Single Cash Flows 4.7 Relating a Uniform Series (Annuity) to its Present and Future Equivalent Values 4.10 Equivalence Calculations Involving Multiple Formulas 4.11 Uniform (Arithmetic) Gradient of Cash Flows 4.12 Geometric Sequences of Cash Flows 4.14 Nominal and Effective Interest Rates 4.15 Compounding More Often than Once per Year 4.16 Interest Formulas for Continuous Compounding and Discrete Cash Flows 4.17 Case Study – Understanding Economic “Equivalence” 5.3 The Present Worth Method 5.4 The Future Worth Method Instructions: • For full credit, begin each calculation with an appropriate formula, show accurate calculations and appropriate units, and clearly identify your answers. Computer-generated submissions are recommended (but not required). You can write mathematical equations in MS Word and export them to pdf file. See https://support.office.com/en-us/article/Write-insert-or-change-an-equation-1d01cabcceb1-458d-bc70-7f9737722702 • • Please be sure your work is neat and legible, not scribbled or squeezed into the white spaces and margins of the assignment sheet. Answer all sub questions (if any) of a problem for full credit for that problem. 1. Try Your Skills 4-E Jonathan borrowed $10,000 at 6% annual compound interest. He agreed to repay the loan with five equal annual payments at end-of-years 1-5. How much of each annual payment is interest, and how much principal is there in each annual payment? (See section 4.4 of the textbook) 2. Try Your Skills 4-J In 1803, Napoleon sold the Louisiana Territory to the United States for $0.04 per acre. In 2017, the average value of an acre at this location is $10,000. What annual compounded percentage increase in value of an acre of land has been experienced? (See section 4.6 of the textbook) 3. 4-137 When you were born, your grandfather established a trust fund for you in the Cayman Islands. The account has been earning interest at the rate of 10% per year. If this account will be worth $100,000 on your 25th birthday, how much did your grandfather deposit on the day you were born? (See section 4.6 of the textbook) (a) $4,000 (b) $9,230 (c) $10,000 (d) $10,150 (e) $10,740 4. 4-139 Your monthly mortgage payment (principal plus interest) is $1,500. If you have a 30-year loan with a fixed interest rate of 0.5% per month, how much did you borrow from the bank to purchase your house? Select the closest answer. (See section 4.7 of the textbook) (a) $154,000 (b) $180,000 (c) $250,000 (d) $300,000 (e) $540,000 5. 4-32 An outright purchase of $20,000 now (a lump-sum payment) can be traded for 24 equal payments of $941.47 per month, starting one month from now. What is the monthly interest rate that establishes equivalence between these two payment plans? (See section 4.7 of the textbook) 6. 4-59 A sum of $10,000 now (time 0) is equivalent to the following cash-flow diagram. What is the value of $B if the annual interest rate is 4%? (See section 4.10 of the textbook) 7. 4-140 Consider the following sequence of year-end cash flows. EOY 1 2 3 4 5 Cash Flow $8,000 $15,000 $22,000 $29,000 $36,000 What is the uniform annual equivalent if the interest rate is 12% per year? (See section 4.11 of the textbook) (a) $20,422 (b) $17,511 (c) $23,204 (d) $22,000 (e) $12,422 8. 4-142 Bill Mitselfik borrowed $10,000 to be repaid in quarterly installments over the next five years. The interest rate he is being charged is 12% per year compounded quarterly. What is his quarterly payment? (See section 4.15 of the textbook) (a) $400 (b) $550 (c) $650 (d) $800 9. 4-143 Sixty monthly deposits are made into an account paying 6% nominal interest compounded monthly. If the objective of these deposits is to accumulate $100,000 by the end of the fifth year, what is the amount of each deposit? (See section 4.15 of the textbook) (a) $1,930 (b) $1,478 (c) $1,667 (d) $1,430 (e) $1,695 10. Try Your Skills 5-Q After graduation, you have been offered an engineering job with a large company that has offices in Tennessee and Pennsylvania. The salary is $55,000 per year at either location. Tennessee’s tax burden (state and local taxes) is 6% and Pennsylvania’s is 3.07%. If you accept the position in Pennsylvania and stay with the company for 10 years, what is the FW of the tax savings? Your personal MARR is 10% per year. (See section 5.4 of the textbook) 11. Try Your Skills 5-S Refer to the following table of cash flows. What is the annual worth of these cash flows over 16 years when i = 5% per year? (See section 5.5 of the textbook) End of year 0 4 8 12 16 Cash flow $5,000 $5,000 $5,000 $5,000 $5,000 12. 5-22 What are the present worth PW and future worth FW of a 20-year geometric cashflow progression increasing at 2% per year if the first year amount is $1,020 and then interest rate is 10% per year? (See section 5.4 of the textbook) Factor Name (F/P, i, N) Single payment compound amount factor Moves a single payment to N periods later in time (P/F, i, N) Single payment present worth factor Moves a single payment to N periods earlier in time (A/F, i, N) Sinking Fund factor Takes a single payment and spreads into a uniform series over N earlier periods. The last payment in the series occurs at the same time as F. (F/A, i, N) Uniform Series Compound Amount factor Takes a uniform series and moves it to a single value at the time of the last payment in the series. Capital Recovery Factor Takes a single payment and spreads it into a uniform series over N later periods. The first payment in the series occurs one period later than P. Uniform Series Present Worth Factor Takes a uniform series and moves it to a single payment one period earlier than the first payment of the series. Arithmetic Gradient Present Worth Factor Takes a arithmetic gradient series and moves it to a single payment two periods earlier than the first nonzero payment of the series. Arithmetic Gradient to Uniform Series Factor Takes a arithmetic gradient series and converts it to a uniform series. The two series cover the same interval, but the first payment of the gradient series is 0. (A/P, i, N) (P/A, i, N) (P/G, i, N) (A/G, i, N) Formula Purpose
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Explanation & Answer

Attached.

Topics:

















4.1 Introduction
4.2 Simple Interest
4.3 Compound Interest
4.4 The Concept of Equivalence
4.5 Notation and Cash-Flow Diagrams and Tables
4.6 Relating Present and Future Equivalent Values of Single Cash Flows
4.7 Relating a Uniform Series (Annuity) to its Present and Future Equivalent Values
4.10 Equivalence Calculations Involving Multiple Formulas
4.11 Uniform (Arithmetic) Gradient of Cash Flows
4.12 Geometric Sequences of Cash Flows
4.14 Nominal and Effective Interest Rates
4.15 Compounding More Often than Once per Year
4.16 Interest Formulas for Continuous Compounding and Discrete Cash Flows
4.17 Case Study – Understanding Economic “Equivalence”
5.3 The Present Worth Method
5.4 The Future Worth Method

Instructions:


For full credit, begin each calculation with an appropriate formula, show accurate
calculations and appropriate units, and clearly identify your answers. Computergenerated submissions are recommended (but not required). You can write mathematical
equations in MS Word and export them to pdf file. See
https://support.office.com/en-us/article/Write-insert-or-change-an-equation-1d01cabcceb1-458d-bc70-7f9737722702




Please be sure your work is neat and legible, not scribbled or squeezed into the white
spaces and margins of the assignment sheet.
Answer all sub questions (if any) of a problem for full credit for that problem.

1. Try Your Skills 4-E
Jonathan borrowed $10,000 at 6% annual compound interest. He
agreed to repay the loan with five equal annual payments at end-of-years 1-5. How much of
each annual payment is interest, and how much principal is there in each annual payment?
(See section 4.4 of the textbook)
The annual payment made will be:
𝑟∗(1+𝑟)𝑛

annual payment = P*(1+𝑟)𝑛−1 = 10,000 *

0.06∗(1+0.06)5
(1+0.06)5 −1

= 2,373.96

Amortization ...


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