Nominal and Effective Interest Rates - Engineering Economics Lightboard

Engineering Economics, Nominal and effective interest rates; compound interest; compounding period; effective rate; effective yearly rate; nominal interest rate; compounded quarterly

[@ZaChousenWan]

Writing backwards. Now that's a skill.

[@EngineeringEconomicsGuy]

Yes! I should add it to my Linked-In profile - lol. (of course, I'm not actually writing backwards in the videos...they're flipped by the camera software)

[@ZaChousenWan]

@@EngineeringEconomicsGuy Ohh I see. Still pretty cool though.

[@EngineeringEconomicsGuy]

Glad you like the videos! I hope they help you understand the concepts.

[@jello2233]

It's funny when you realize how easy it is to forget basic principle in a field, considering that I am about to start a MBA in finance, and I am here trying to remember my finance 101 for my final!

[@EngineeringEconomicsGuy]

Ha! Don't worry - things like nominal and effective interest rates are easy to forget - unless you use them every day! I hope you find the videos useful. All the best in your MBA (I completed an MBA many years ago!). Good luck!

[@jello2233]

@@EngineeringEconomicsGuy Thank you it is really appreciated, and even more for the video!!

[@carsonp6117]

Happy Birthday Engineering Economics Guy! Thanks for all your help, hope your day is great :)

[@EngineeringEconomicsGuy]

Ha! Thanks a lot!! Happy to know my Channel has helped you.

[@taekwondotime]

The way I remember them is as follows: NOMINAL = The annual interest rate. EFFECTIVE = The equivalent annual interest rate you would need to generate the same amount of interest accumulated without the compounding.

[@EngineeringEconomicsGuy]

Ok! Good way to put it.

[@KT-dj4iy]

I'm closing on a house right now, and I was stumped by this for a few days as I tried to get my calculations of monthly payments to match what my lender was saying. They were doing what almost everyone does when they want to convert a yearly interest rate, Y%, to a monthly one, M%, which is to divide it by 12 (for your typical domestic mortgage). But I also thought that was just an approximation because I know that the "correct" way to convert is not: M% = Y%/12 But rather: M% = (1+Y%)^(1/12) - 1 But eventually I discovered what this video is confirming, that I was assuming that the annual rate the lender was stating was the _Effective_ rate, when in fact it was this _Nominal_ rate (which I'd never heard of). So, I now understand the math, but I still don't understand _why_ they do it this way. If someone says they will charge me 10% interest per year on money I borrow then if I borrow $1,000 and make no payments, then I will expect that balance to have grown to $1,100 by the end of the year _regardless_ of how it is being compounded. But in reality they are pretty much always "lying" when they state that nominal annual rate because unless it is only compounding annually, the amount I owe at the end of the year will be _more than_ my prediction of $1,100. OK, obviously they're not really lying. But but why do they state it that way?

[@EngineeringEconomicsGuy]

Excellent question, and excellent observations! It does given the appearance of lying when interest rates are quoted using the nominal rate. I had the same feeling when I first discovered this. There are 2 answers to your question; a simple answer, and a much deeper math-based answer. Simple answer: Quoting a nominal rate is the convention the financial world uses - you just need to learn it. Better answer: The practice of quoting a nominal rate reveals it's "correctness" when the number of compounding periods approaches infinity! (?!?) Have a look at my video on Continuous Compounding. Jacob Bernoulli actually discovered the value of 'e' (Euler's Number), through an exploration of nominal and effective interest. The Wikipedia entry for Euler's Number also has some good info. Hope this is what you were looking for!

[@KT-dj4iy]

@@EngineeringEconomicsGuy excellent! Thanks for responding so quickly too. Because this video is several years old, I hadn't held out much hope that you'd respond at all, but I checked and saw that you had recently posted others so I took a chance you might still be around. Im glad I did! Your range of topics looks fascinating to me. I'm a Physics & CompSci guy now running an engineering consulting firm, and while my background gives me the ability to handle the mathematics of business, I often bump into the fact that there is often more *to* the quantitative side of business than just the math. It often occurs to me that if I was going to do it all again, I might choose a technical financial education route, rather than a so-called STEM one. I love finding where deeper math influences real-world finance and accounting just as much as it does the world of physics and computation. Good stuff; I'll definitely follow the pointers you gave; and you have a new subscriber. Cheers!

[@ymonpaulo]

Are you really writing backwards? 🤔

[@EngineeringEconomicsGuy]

Ha! No, I'm using software to horizontally flip the video.

[@saibharadwajvenati3709]

Thanks for the lesson. Life lesson - if u r giving credit, compound it as frequently as possible. If u r taking credit, make sure it compound frequency is very low

[@EngineeringEconomicsGuy]

You've got it!

[@ashish835]

brother this behaviour is haram

[@KT-dj4iy]

It looks like the rule for giving credit is actually, _"compound it as frequently as possible but don't tell the borrower that, and hope they haven't watched this video"_

[@NgoshaRambuda]

This guy is brilliant, you actually helped me a lot

[@EngineeringEconomicsGuy]

Great to hear! Thanks for the comment, and good luck in your course!

[@rayraymukhi230]

Wow, he should teach a lecture on Professional Communications

[@EngineeringEconomicsGuy]

Thanks for the comment!

[@hamzajamal9522]

Thank you very much sir. Really cleared the topic for me

[@EngineeringEconomicsGuy]

You're welcome!

[@ahmadelmahallawy8739]

What if we want the effective semi-annual rate? What do we do? Thanks!

[@EngineeringEconomicsGuy]

Good question! Go to the time about 9:50:00 in the video and watch my explanation of the 'formula' for effective interest, BUT, instead of raising the term (1+(r/m)) to the power of 'm', you would raise it to the power of 'n', where we define 'n' as the number of compounding periods in a 'half-year' - i.e. semi-annually. In this example, 'n' =2 since there are 2 quarters in a half-year. Hope this helps!

[@plzcorrectmygrammarimlearn86]

Thanks your lessions are accually useful!!! love from Thailand

[@EngineeringEconomicsGuy]

Thank you!

[@christinemambo1319]

Brilliant explanation thanks so much sir 🙏

[@EngineeringEconomicsGuy]

You are very welcome! Thank you for the comment.

[@unknown-td4zy]

dont you think you should also tell when should be using nominal interest rate and effective interest rate..

[@EngineeringEconomicsGuy]

It is a good idea to clarify this point - thanks. Always use the effective interest rate that matches the frequency of the payments in calculations. ..meaning, if your problem has monthly payments you must use the effective monthly interest rate. The nominal rate is usually the information you are given in the problem, but this needs to be converted to the effective rate before doing the calculations. I hope this helps! Please explore some of my other videos to familiarize yourself with the procedure.

[@ayabongazungu8332]

Great lesson and I love the colour of pen you are using.

[@EngineeringEconomicsGuy]

Glad you like it!

[@Pages_Perfected]

Thank you so much you are awesome

[@EngineeringEconomicsGuy]

No problem

[@BlackMambaKO]

The question I have is why would there even be nominal interest rate? To me it would be logical to have annual interest rate and to take root of it by the number of times it compounds so we get periodical interest rate and this would give us same interests. Nominal interest rate is never used unless you calculate interests yearly.

[@EngineeringEconomicsGuy]

Excellent question. This also bothered me when I was a student. It turns out that quoting a "nominal" rate over some number of "compounding periods" is actually the best way to do it! From a mathematical viewpoint, as the number of compounding periods increases to infinity, the effective interest rate becomes e^r... yes, Euler's Number raised to the NOMINAL interest rate. This fact was powerful enough to convince me that the seemingly illogical way of quoting interest rates IS ACTUALLY the right way to do it! I explain this in my video on 'continuous compounding': kzbin.info/www/bejne/gqnZdHmKqNGJsJY It dates back to Jacob Bernoulli and the discovery of Euler's number! I hope this helps!

[@BlackMambaKO]

@@EngineeringEconomicsGuy I checked linked video out but e^r is just yearly compounding with infinity. That still means nominal interest is divided by number of compoundings ^ number of compounding. Which still doesn't explain why nominal value is divided with number of compoundings instead of rooting it? This way our compounded G would be the same regardless of how many times it would compound in a year.

[@EngineeringEconomicsGuy]

The method or convention of quoting a Nominal (yearly) rate with some compounding frequency (i.e. daily, monthly, semi-annually, etc.) is simply the convention the world has decided to use. My example with an infinite number of compounding periods (e^r) justifies this convention (at least it does for me). You are suggesting that we ONLY using true-effective-interest-rates for all periods - this is very sensible...but it is simply not how things are done.

[@EngineeringEconomicsGuy]

Maybe this is a better way to think of it: You can tell me the effective interest rate for any period (i.e. - a month, day, week, etc.) - but you can't tell me the effective interest rate for an infinitely small time period. It would be tempting to conclude that the effective interest rate would approach zero for an infinitely small time period... but this can't be true - there must be some amount of interest. Using a nominal rate and specifying the number of compounding periods allows the number of compounding periods to become infinitely small, but still gives a reasonable effective interest rate: e^r. Euler's number is fundamentally related to growth of any kind - in Nature, or with money!

[@BlackMambaKO]

@@EngineeringEconomicsGuy if it is convention that was just decided to be like it is then ok. I thought it was important to get same interests in a year regardless of how many times they compound.

[@sitizahrazahirah537]

I like the way you explaned using lightboard, how its works?

[@EngineeringEconomicsGuy]

Check out this video I recorded last year that explains the Lightboard: kzbin.info/www/bejne/a3uugWqOgZqhrLs

[@tracy1284]

Thank you soo much😊😊

[@EngineeringEconomicsGuy]

Most welcome 😊

[@kumarbanjara7229]

than you sir

[@EngineeringEconomicsGuy]

I appreciate the thanks!

[@faizwazir9180]

Great sir

[@EngineeringEconomicsGuy]

thanks!

[@ISwifty900]

Thank you, may god bless you sir

[@EngineeringEconomicsGuy]

Thank you for the kind comment. Good luck in your course!

[@lojain822]

First, thank you for your explanation. Second, can you please make a video about advices how to get ready to the exams? it would be very helpful if there’s any tips to be fully ready to take an exam☺️ thank you again 🙏🏻.

[@aidos4381]

Awesome. thanks a lot.

[@EngineeringEconomicsGuy]

You're welcome!

[@AJ-et3vf]

Great video! Thank you!

[@EngineeringEconomicsGuy]

Glad you liked it!

[@keeganlupunga2874]

awesome video on nominal interest such a good lecture