Arithmetic Gradient - Engineering Economics Lightboard

[@genetalavera4256]

It's a little weird not giving the equation for the a given g , i , n. I guess we have different schools though but for board exams we do not have the tables. Thanks for the explanation though

[@EngineeringEconomicsGuy]

You make a good point. I could have given the formula for the (A/G, i, N) factor! It probably comes up somewhere else in one of my other videos - BUT, for the benefit of anyone looking for it...it's a complicated one: [ 1 / i ] - [ N / (( 1 + i )^N - 1)] There are other forms, but this is the most compact. I will "pin" this comment to the top of the list so anyone looking for the formula can hopefully find it. Thanks for the comment. Good luck on your Board Exams!

[@davidruiz2656]

This video solved all my headaches. Thanks Engineering economics guy!! My teacher spent a whole 3 hour lecture trying to explain this and you do it 10 times better in 11 minutes

[@EngineeringEconomicsGuy]

Hey - thanks for the kind words!

[@evanhuang6963]

How come u have only 150 subscribers. you are the best problem explain KZbinr i have never seen. I watched lots of engineering classes material from youtube. You are definitely the best. very clear and looks fantastic. be real, i love your videos. no idea how could you not have subscribers.

[@EngineeringEconomicsGuy]

Thank you for the very kind words!! I'm sure more subscribers will come. My channel is still new! Please tell your course instructor about my site. I welcome all instructors and students.

[@evanhuang6963]

Engineering Economics Guy i did I post your link in to group chat, wish class mate go and watch your lecture.

[@EngineeringEconomicsGuy]

Thanks!!

[@EngineeringEconomicsGuy]

Alicia - good question! The formula for (P/A, 5%, 5) is: [(1 + i)^N - 1] / [ i * (1 + i)^N], where i=5% and N=5 (and * means multiply, / means divide, and ^ means raise to the power). The formula for (A/G, 5%, 5) is: [1 / i] - [ [N] / [(1 + i)^N - 1] ]. It is easy to use so-called 'compound interest tables' to obtain these values; just find the compound interest table for " 5% " and you will see the columns for P/A, A/G, etc. and the rows in the table are for different values of N. I hope this helps! I also have other videos that explain these - please explore my Channel.

[@safeegull22]

I am gonna subscribe, because you solved my problem, I failed in exam , because my teacher lost my answer sheet, my head was burning, now I never go her class to attend, I get benifit from you, and you are the best explainer ever I seen, I seen lot of videos,, I understand lot of things, but you are the best

[@EngineeringEconomicsGuy]

Thank you for the great comment! Your compliments are very motivating for me! (I'm sorry to hear about your exam) - all the best!

[@kachipakitv9899]

Sir your channel is best for engineering economics, please make new videos and cover all topics

[@EngineeringEconomicsGuy]

Thank you! I'm working on it!

[@yasseredza5620]

Thank you so much❤ this is the best tutorial I found for this topic.❤

[@EngineeringEconomicsGuy]

Glad it was helpful!

[@acelee8759]

High quality vid sir! We have an exam tomorrow in Engineering economics. Much love from the Philippines ❤

[@EngineeringEconomicsGuy]

I'm glad you liked the video! Good luck tomorrow!!

[@furikuri6427]

Very clear and informative! Great work sir

[@EngineeringEconomicsGuy]

Glad it was helpful!

[@kfoxx3]

It is absolutely pathetic that we have to resort to youtube for a college education. Thank you so much for doing this.

[@EngineeringEconomicsGuy]

You're so welcome! Good luck in your course.

[@1622roma]

WOW. You sir are too good.

[@EngineeringEconomicsGuy]

Thanks a lot!

[@kacydunlap9309]

Hello sir, I was wondering how you got 5%? I kept rereading the initial problem, and I couldn't find it or figure out how you calculated it. I apologize if this is a dumb question. Thank you for your content it is extremely helpful.

[@EngineeringEconomicsGuy]

Kacy - GOOD QUESTION! I think that the 5% was left off the text in the problem shown at the beginning of the video - oops! At time 5:35 (approx.) in the video I say, "we were also told in the problem that the i=5%". So to answer your question; I didn't calculate i, it was actually given in the problem. Sorry it was left out of the pop-up text!

[@DavidLowrimore]

I get confused when there is a gap between present and future gradient. What do we do when questions say '8 years after depositing, you want to withdraw $1000 decreasing 5% every year at 10% interest?' Or when questions have a negative annuity in the past and a positive gradient overlapping but going 3 years past the annuity?

[@EngineeringEconomicsGuy]

David, yes, there can definitely be some difficult scenarios with gradient series. I don't have a video for the cases you're talking about, HOWEVER, the key to solving difficult problems is to have a strong grasp of the fundamentals. I recommend this video: kzbin.info/www/bejne/qmTMaIJ8jN18hJo You should focus on the patterns of the cash flows. Once you understand the patterns, you can mix multiple compound interest calcs to get the answer you need. For example, if you have a gradient that starts at some time in the future, you can find an equivalent 'P' or 'F' at the point in the future that matches the G pattern, then use an F/P factor or a P/F factor to move th 'P' or 'F' amount to whatever TIME you want. My video on 'equivalence' might also be helpful! kzbin.info/www/bejne/aH2zmJJ-orWqmJY Good luck!

[@karamghaddar3946]

Amazing videos sir, one question tho is why don't we just use the formula P = (P/G, I, n) to calculate P2, I tried it and got the exact same result!

[@EngineeringEconomicsGuy]

Karam, yes, you can absolutely use the P/G factor for P2! Thanks for pointing this out. Unfortunately, some textbooks don't have a P/G factor - including the one I use! This is why I use the 2-step process of A/G then P/A - all texts have these 2 factors. Note: If you multiply A/G x P/A you get the value of P/G! Thanks for watching! And, thanks for this great comment!

[@karamghaddar3946]

@@EngineeringEconomicsGuy Thank you for your answer and for the note!! You're doing an amazing job to lots all across the globe, I've been watching your channel since the morning and I am really grateful for you and for your perfect explanations. God bless you. Thank you again, have a great great day!!

[@EngineeringEconomicsGuy]

Thank you for the wonderful comment! Good luck in your class!!

[@chris5019]

I am in the middle of studying for my PE license and this is an important section in the exam. The confusion that I am having with the gradient series is the n value. When solving a cash flow diagram involving a gradient series, wouldn't n for G = n - 1 since the gradient starts at year 2? Maybe I am getting confused with the generic diagram that shows the 0g, 1g, 2g ... all the way to (n - 1)G for the final gradient. Is this not the same case for the n value in years used in the calculation? In the example you did in this video, I would have said the n value for G was 4 since it starts at year 2 (and the total period was 5 years). Is there any circumstance where this is correct?

[@EngineeringEconomicsGuy]

The Gradient DOES in fact start at n=1 but with a value of zero! Confusing...yes!!! I think of it like this: The gradient is a triangle that starts with its tip at n=1 (so the height is actually zero at n=1, but the triangle starts nonetheless!). Most books, and this video, explain it as starting with 0G (zero-G). Just ensure you realize this example has 2 components: A gradient (triangle), AND an underlying regular annuity (rectangle). Hope this clarifies.

[@chris5019]

Makes perfect sense now. Thank you for that clarification!@@EngineeringEconomicsGuy

[@EngineeringEconomicsGuy]

Happy to help! (Be sure to "Like" and "Subscribe" as they say!! It really helps my views and the KZbin algorithm.)

[@nanaadomnyarko6472]

From your illustration, the maintenance costs are expenses. Why are they represented on the positive side of the cashflow diagram?

[@EngineeringEconomicsGuy]

Excellent, excellent question! I should probably put a note on the video or something. The question is worded such that the car owner 'sets aside' - i.e. - 'invests' money at time t=0 to cover all of these future costs. The cash flow diagram is drawn to reflect the fact that he 'receives' these yearly payments from his initial investment. The wording and setup of the problem is a little weird and I even debated myself about which way to draw the arrows! I decided that the main purpose of the video is to teach 'G', so I'm ok with the way that I've done it, BUT, as a general rule you are correct, 'costs' should be down arrows. I hope you will accept this explanation! EEGuy.

[@nanaadomnyarko6472]

@@EngineeringEconomicsGuy understood. I get your explanation

[@nanaadomnyarko6472]

I would be grateful if you do a video on shifted series, especially shifted gradient series. I love your explanations

[@EngineeringEconomicsGuy]

Thanks very much! I'm glad you like the videos. Maybe my video on 'equivalence' would be helpful to you? kzbin.info/www/bejne/aH2zmJJ-orWqmJY Thanks for watching!

[@shuraplays214]

To anyone out there studying engineering economics. Don't be like me studying 3 hours before the exam😅. Don't procrastinate!!

[@EngineeringEconomicsGuy]

Great Advice!!

[@EngineeringEconomicsGuy]

I hope the videos helped - let us know how it went!

[@shuraplays214]

It went well! I hope so. One of the problems was literally about this topic but the difference is that it's Pt = Pa - Pg. I was able to understand and answer it because of this. Thank you!

[@AyaanKhan-ei3gk]

Thank you so much sir I JUST wanted to ask one question from you , the time value of money, when we have annuity payments,we find out their present worth ,to compare with the investment we made in year 0 ,to check if the investment gives us a return?am i right to assume this as the time value of money?

[@EngineeringEconomicsGuy]

Yes, I would say your statement is generally correct. However, I fear you might be confused with the meaning of the phrase "time value of money". This is a very broad phrase meaning the following: Dollar amounts paid or received at different points in time need to have their value adjusted by an interest rate. The concept of the time value of money hinges on the idea that a dollar today is not worth the same as a dollar a year from now. IGNORING inflation or deflation, the dollar today is worth more than the dollar a year from now, because, if I received the dollar today, I can invest it and earn interest. One year from now, that dollar I received will be worth something more; maybe $1.08, depending on what I invest it in. This broad general concept is what is meant by the phrase 'time value of money'.

[@cestlavieeee]

What I totally don't get, is for p2, you do P2 = G(A/G)*(P/A) Now, I know here we are going from finding A and using that value to find P. To find A, we do G(A/G), and that result is our A. Then do find P, we do (P/A) but we dont multiply by A? Why dont we multiply it like we always do? In this case, the formula should be P2 = G(A/G)*A(P/A), but of course its not, but why not? Where does that A just disappear?

[@EngineeringEconomicsGuy]

We split the problem into 2 parts: 1) the G and 2) the underlying A. Think of them as the triangle and the rectangle. For the 'triangle', (the G) we don't need to multiply by the A, that is calculated in the other 'part' of the question. But, notice that we add the P1 and P2 at the end. Hope this explains it. The video is correct.

[@nicolascorrea2664]

amazing video

[@EngineeringEconomicsGuy]

Thanks!

[@anyone779]

Sir, how (P/A, 5%, 5) = 4.3295 ? How to input this to Scientific Calculator? 😅 I understand everything in this video I just don't know how to input (P/A,5%,5) and (A/G, 5%,5) in sci cal😅.

[@EngineeringEconomicsGuy]

Alicia - good question! The formula for (P/A, 5%, 5) is: [(1 + i)^N - 1] / [ i * (1 + i)^N], where i=5% and N=5 (and * means multiply, / means divide, and ^ means raise to the power). The formula for (A/G, 5%, 5) is: [1 / i] - [ [N] / [(1 + i)^N - 1] ]. It is easy to use so-called 'compound interest tables' to obtain these values; just find the compound interest table for " 5% " and you will see the columns for P/A, A/G, etc. and the rows in the table are for different values of N. I hope this helps! I also have other videos that explain these - please explore my Channel.

[@anyone779]

@@EngineeringEconomicsGuy Thank you very much sir.

[@EngineeringEconomicsGuy]

You're Welcome!

[@yaserc.3363]

brilliant , many thanks❤

[@EngineeringEconomicsGuy]

You are most welcome!

[@tamida5060]

I have taught my students with this simple way, but I'm still confused what if the aritmetic gradient is fluctuative within period, for instance, we have 10 years for bussiness periode, 4 years from present the gradient value increased, and then 6 years ahead the gradient value decreased. What wil be sir?. Thank in advance

[@EngineeringEconomicsGuy]

Thanks for the question. I'd be happy to help but the solution you're seeking is too complicated to describe here. Please email me at [e-mail] and I will help you!

[@Pages_Perfected]

You Are Awesome

[@EngineeringEconomicsGuy]

Thanks!

[@krystalvang9659]

How did you get 4.3295?

[@EngineeringEconomicsGuy]

4.3295 comes from the 5% compound interest table in the P/A column in the row for 5 periods. You can also use the P/A formula. Have a look at some of my other videos on 'Compound Interest Factors' for a more complete answer. Thanks for the question! Good luck in your course!

[@danhthaitran8034]

how about the decrease gradient problem sir ?

[@EngineeringEconomicsGuy]

Good question! Sorry, I haven't recorded a video with a declining G. I'll put it on my list of things to record. In the meantime, I can offer the following advice: The underlying 'regular' annuity will have a value of 'A' which is the value of the cash flow at time t=1 (don't worry that the values are declining, we will look after that!). The value of G will be the constant amount of the decline in the cash flows each time period. Rather than adding the present value of the G 'triangle' to the present value of the regular underlying annuity - You Subtract it!... So, using this video as an example, the final value of 'P' would be 'P1' minus 'P2', where 'P2' is the value of G(A/G, i, n)(P/A, i, n). Hope this helps!

[@seanburton5298]

@@EngineeringEconomicsGuy not really because another version of this question is to find that G value such that a specific amount is invested for efficiency improvements in a machine and you want to get a specific return in the cost reduction of manufacturing, therefore, what is the G-value to recover your investment and realize a 14% return on that investment due to lower manufacturing costs because of your investment?

[@EngineeringEconomicsGuy]

This would be a different type of problem. If the "shape" of the cash flow diagram is the same as this example but with an unknown 'G', then you can still create a 'time-value-of-money' equation that is of the same form as this example. To solve for the unknown G you would need to be given the value of P (and you would use 14% as the interest rate).

[@vixYtor]

Sir, isn't maintanace outflow?

[@EngineeringEconomicsGuy]

YES! However, the way the problem is setup is a little strange! The problem is asking 'what amount of money needs to be set aside TODAY to payout the required $ amounts to cover the future maintenance costs?'. For this reason, I've structured the cash flow at t=0 as a down arrow (money is coming OUT of your pocket - i.e. -you are investing it somewhere); and the 'payouts' of this 'investment' as up arrows (you are RECIEVING the money from your original t=0 investment). Of course, you then use that money to PAY the maintenance costs but that step is not part of the cash flow diagram. I know it's a little confusing. Hope this helps!

[@ptiinsafstudent2778]

Great

[@EngineeringEconomicsGuy]

Thanks!

[@walterbaldemor2128]

Is it like an arithmetic progression?

[@EngineeringEconomicsGuy]

Yes. Same kind of series.

[@chiekeuzodinma3254]

Sir my lecturer subtracted 1 year P/A from the total year (5) That you solved here to give P -1 Pls what the difference

[@EngineeringEconomicsGuy]

The P/A compound interest factor works when the first "A" occurs at t=1. I suspect your lecturer might have been doing a problem with an "A" starting at t=0...? Look carefully at the problem and let me know if this comment helps you figure it out!

[@chiekeuzodinma3254]

@@EngineeringEconomicsGuy yh exactly

[@EngineeringEconomicsGuy]

Happy to help!

[@gabewinter9406]

is rhe A/G factor an integration?

[@EngineeringEconomicsGuy]

No, it is one of many common 'compound interest FACTORS'. It is derived from a combination of the A/P factor and the P/G factor - sorry for the jargon! Have a look at my other videos on cash flows and the time value of money. These factors such as A/G are read as "A given G". If you multiply the value of the 'Gradient' (G) by the factor called "A given G", you get the value of the recurring Annuity (A).

[@timilehinonalaja1540]

Great video, thanks for this sir. Please can you kindly explain Example 6.7 in Engineeering Economics by Leland Blank & Anthony Tarquin sir.

[@timilehinonalaja1540]

The operational phase: why do we have the (P/F, 18%,8) multiplied by the arithmetic gradient. Thanks in dvance sir.

[@EngineeringEconomicsGuy]

The Geometric gradient gives you the PW of the 8 years of costs that are increasing by 4% per year starting at $200k, BUT but this "PW" will actually be positioned at t=2 (not t=0) since the first $200k cost occurs at t=3. I strongly suggest you draw a cash flow diagram. This PW (at t=2) needs to then be multiplied by the (P/F, 18%,2) to bring it back to the 'true' PW at t=0. THEN the whole PW can get converted to an AW with the $ amounts from the other components of the problem. Read this explanation very carefully and draw what I'm talking about... hopefully this answers your question! You can watch my videos on patterns of cash flows if you need to...

[@EngineeringEconomicsGuy]

kzbin.info/www/bejne/pILYhp16qs6fd9k

[@Azakadune]

Should have given the A/G formula to find the factor. Anyone needs it, it is (1/i)-(N/((1+i)^N-1)

[@EngineeringEconomicsGuy]

Thank you! Yes, that is the correct formula for A/G. Note that it is the product of the A/P and P/G formulas! Thanks for watching and contributing!

[@Azakadune]

@@EngineeringEconomicsGuy ah yes, I only noticed because I’m watching as review and to make my formula sheet for the midterm exam. Your videos are great and honestly much easier to understand than my professor’s in class lectures.

[@EngineeringEconomicsGuy]

Thank you for the kind words! I've taught this course for about 10 years. I made most of my videos in 2016 and 2017 and just uploaded them to KZbin at the beginning of the COVID shutdown. Some of my videos are clips from my live Zoom classes recorded during COVID. I might be the only KZbinr whose videos were NOT recorded FOR KZbin...they were recorded for my students!

[@AloneBoy-lp7cx]

8:18 confusion gone tnx

[@EngineeringEconomicsGuy]

Excellent! Happy to help.

[@seanburton5298]

What if you are not given G?

[@EngineeringEconomicsGuy]

This would be a different type of problem. If the "shape" of the cash flow diagram is the same as this example but with an unknown 'G', then you can still create a 'time-value-of-money' equation that is of the same form as this example. To solve for the unknown G you would need to be given the value of P.

[@mananshah7805]

I used a different logic and getting a completely different answer. Please tell me where I am wrong. My interpreation of the problem is that we know by end of 5 years the guy will need $900, so I am supposed to find how much money should he invest in the bank today @5% interest, so that by end of 5 years the total in his bank account in $900. In this scenario if I invest about $675 then at the end of 5 years I have $905 in my account. Y1 Start: 675 | Y1 end: 709 Y2 Start: 709 | Y2 end: 744 . . Y5 Start: 861.5 | Y5 end: 905 Please tell me where my understanding is wrong and without using the formulae, how can you intuitively explain what does 766.64 mean.

[@EngineeringEconomicsGuy]

Sorry, this is a time value of money problem. That means you cannot simply add and subtract dollar amounts that occur at different points in time. Before you tackle a problem such as the one in this video, please review some of my other videos on understanding the time value of money and patterns of cash flows. This type of financial math works differently from what you are probably used to. Q: Would you rather have $100 today, or $100 a year from now? A: You would rather have the $100 today so you can earn interest for the year...making $100 today Worth More than $100 a year from now. Please take some time to digest this fundamental concept.

[@mananshah7805]

@@EngineeringEconomicsGuy Okay, now I understand. So basically for paying 120 next year I put $114.29 NOW in the bank. Similarly to pay 150 after 2 years I put $136.05 NOW in the bank, and so on. And then when I add everything I am putting now in the bank i.e. (114.29, 136,05, 155.49, 172.11, 188.05) we get $766.64. Thank you soo much for replying back!

[@EngineeringEconomicsGuy]

You've got it!! Exactly correct - well done. Good luck in your course!

[@JordanBarclay]

please take all of my subscribers you deserve it.

[@EngineeringEconomicsGuy]

Jordan - thank you! I really appreciate the comment. I just subscribed to your Channel (very nice). If you can send some of your viewers in my direction I would greatly appreciate it!