Eng'gEcoReview

7/30/2019 Eng'gEcoReview

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Engineering EconomyReviewer


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Find P or F from Single Amounts

How to do it: The simplest problems to solve in engineering economic a

those which involve finding the value of a single amountof mearlier or later date than that which is given. Such problems invthe future worth (F) of a specified present amount (P), or vice veproblems involve using the equations:

F = P(1 + i)n or P = F[1/ (1 + i)n]In terms of standard factor nequation on the left is represented as F=P(F/P,i,n) and the equaright is represented as P = F(P/F,i,n).


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Find Present Worth (P)Example: #1: A person deposits P5,000 into a money market account which pay

of 8% per year. The amount that would be in the account at the end of ten years a. P2,792 b. P9,000 c. P10,795 d. P12,165

Solution: Answer: C.

The P5,000 represents a present amount, P. The future amount, F,

F = P5,000 ( F/P, 8%, 10)

= P5,000 [1 / ((1 + 0.08)^-10)]

= P10,794.625


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Find Future Worth (F)

Example #2: A small company wants to deposit a single amount of money nhave enough to purchase a new truck costing P50,000 five years from now. Ibe deposited into an account which earns interest at 10% per year, the amoudeposited is most nearly

a. P10,000 b. P31,050 c. 33,250 d. 319,160


The P50,000 represents a present amount, P. The future amount, F, is

P = P50,000 ( P/F, 10%, 5)

= P50,000 [1 / ((1 + 0.10)^ 5)]

= P31,046.066


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Find P from a Uniform Series (A) and Vice Ver How to do it:

Uniform series cash flows are represented by the symbol A. A unifor

to cash flows which: (1) occur in consecutive interest periods, and (2amount each time. To solve for P for these types of problems, the follis used:

P = A In standard factor notation, the equation is P = A(P/A,i,n). It note in using this equation that the present worth, P, is located oneahead of the first A. It is also important to remember that n must b

number of A values and the interest rate, i, must be expressed in the sas n. For example, if n is in months, i must be an effective interest rate

This standard equation can be used in reverse to convert a preseuniform series amount using the form A = P(A/P,i,n). This, for examdetermine the monthly payment associated with a car purchase or hcompound interest rate of i%.


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Find P from a Uniform Series (A)

Example #3: A company expects the material cost of a certain manufacturingbe $20,000 per year. At an interest rate of 8% per year, the present worth of ta five year project period is closest to:

a. P29,386 b. P56,220 c. P79,854 d. P117,332


P = A(P/A,i,n)

= P20,000 [(1+0.08)^5 1 ) / ((0.08)(1 + 0.08)^ 5)]

= P79,854.201


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Example #4: A piece of machinery has a first cost of $31,000 with a monthly cost of $10,000. If the company wants to recover its investment in five years rate of 1% per month, the monthly income must be closest to:

a. P5,498 b. P6,386 c. 8,295 d. 10,688

Solution: The A value is per month. Answer: D.

A = 31,000 ( A/P, 1%, 60) + 10,000

= 31,000 [ (1+0.01)^60 0.01) / (1+0.01)^60 1 )] + 10,000

= P10,689.578

Find A from a Uniform Series (A) Given P


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Find F from a Uniform Series (A) and Vice Vers

How to do it:

In the previous problem type, the procedure for converting series into an equivalent present amount was discussed. Hereseries is converted into a future amount instead of a presentequation for doing so is:

F = A The standard notation form is F= A(F/A,i,n). It is im

remember that the F occurs in the same period as the last A. the n is equal to the number of A values and the i used in the must be expressed over the same time units as n.

The standard equation can be set up and solved in reverse tovalue from a given future worth, F, using A = F(A/F,i,n).


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Find F from a Uniform Series (A) and Vice Vers

Example #5: If a person deposits P100 per month into an account which payrate of 6% per year compounded monthly, the amount in the account at the eyears would be nearest to:

a. P564 b. P369 c. P6,977 d. P7,992

Solution: Since the cash flow (i.e., A values) occurs over monthly intere

the n and i must have monthly time units. Answer: C.

F = 100 ( F/A, 0.5%, 60)

= 100 [ ((1+0.005)^60 1) / (0.005)]

= 6,977.003


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Find A from a Uniform Series (A) Given F

Example #6: A small company wants to have enough money saved to purchP200,000 warehouse in five years. If the company can invest money at 18% the amount that must be invested each year is closest to:

a. P27,960 b. P36,920 c. P49,650 d. P63,960

Solution: Answer: A.

A = P200,000 (A/F, 18%, 5)

= P200,000 [(0.18) / ((1+0.18)^5 1)]

= P27,955.568


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Identify Nominal and Effective Interest Rates

How to do it: Nominal and effective interest rates are similar to simple and compound inter

a nominal rate being equivalent to a simple interest rate. All of the equations time value of money are based on compound (i.e., effective) rates, so if the inthat is provided is a nominal interest rate, it must be converted into an effectivit can be used in any of the formulas. The first step in the process of insuringeffective interest rates are used is to recognize whether an interest rate is noeffective.

Effective Rate - When no compounding period is given, interest rate is an effewith compounding period assumed to be equal to stated time period while

Nominal Rate - When compounding period is given without stating whether thrate is nominal or effective, it is assumed to be nominal. Compounding period


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Nominal or Effective

Interest Statement Nominal or Effective Compoundin

5% per year compounded monthly Nominal Mo

10% per year Effective Y

Effective 15% per year Effective Mo

compounded monthly

20% per year compounded quarterly Nominal Qua


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