INTEREST: Simple Interest vs Compound Interest vs Continuous Interest

►Play around with the INTEREST CALCULATOR I built using Maple Learn for simple interest, compounded interest, and continuously compounded interest here: learn.maplesoft.com/index.htm...
►Check out MAPLE LEARN for browsers: www.maplesoft.com/products/le...
►Check out MAPLE CALCULATOR phone app : www.maplesoft.com/products/ma...
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Welcome to the first episode of my financial math playlist! Each video we are going to cover one topic related to money, personal finance, investing, or economics. The goal is to break down the mathematical formulas involved in these topics so we can really understand and be smarter with our money.
In this first episode we are going to be talking about interest rates. We will see the formulas for simple interest, compound interest, and continuously compounded interest. We will, for instance, if you have a loan starting with an initial principle, and a particular interests rate over the term of the loan, how much money is owed at the end? Well, it depends on the type of interest. With simple interest, the same interest payment of a fixed percentage is paid every single period. With compound interest however, the amount of interest in each period goes up as there is interest on the interest. We will see how to break down an annual interest rate that is compounded monthly, for instance. Finally, continuously compounded interest is a limit as you compound more and more and more frequently.
0:00 What is interest?
1:20 Simple Interest
5:19 Compound Interest
9:27 Comparing different compounding periods
13:40 Continuously Compounded Interest
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[@DrTrefor]

***TYPO*** At 14:18 I completely drop the P and write just e^rt as opposed to Pe^rt for continuous interest. Doh! Thanks again to Maplesoft for sponsoring today's video, make sure to check out Maple Learn here: www.maplesoft.com/products/learn/?p=TC-9857

[@safeegull22]

Sir this calculator never work

[@utuberaj60]

Yes Dr Bazett. The Amount A = P x e^rt. While explaining the same in Calculus- this Compound Interest formula is invoked first as you did and then set P=1, we get the value of e in the limit as n ---> infinity. Of course this is deduced by actual calculations! Thanks Dr. I would like you to consider explaining in this "Financial Math" video series how calculate the EMI (Equated Monthly Installment) of a mortgage loan used for buying cars, houses etc. No school or College course gives this stuff and all one gets to do is to use the plethora of "Calculator Tools" freely available on the Net. It would be great if you can get down to the Math behind these calcualtions. Looking forward to 1your video in this series. As always, you are the best Math teacher who can explain such the math behind mundane stuff like finance, to advanced calclulus. I enjoy all of it. Keep going Professor!!

[@utuberaj60]

Oh I forgot. You also set r=1 in the formula before getting to e!

[@vladracul40]

I like 👍 your video class, Now I have a BIG QUESTION IF YOU CAN EXPLAINED, not just to me but to everyone who is interested . Here is the question : in all three scenarios you presented in this video, if I want to add the ANUAL INFLATIONARY coefficient, how I can do that knowing that INFLATION is doferent from one year to onother. Thank You very much.

[@annali9577]

I can't believe it, I have followed you since last year and this year I am just starting my finance math course. If I studied it last year I wouldn't have your help. Great as always, thank you

[@EEFTARUNA]

Benjamin Franklin "Money makes money. And the money that money makes, makes money." That is probably the simplest explanation of compound interest you'll ever hear. Albert Einstein " compound interest is the most powerful in the universe "

[@Eduardo-cr8ri]

My interest in your videos: continuous lol

[@DrTrefor]

Lol I wish I could upload continuously to KZbin:D

[@MarcusFred-wn3iv]

After a terrible 2022, shell-shocked financial backers have a lot to think about and losses to recover from. An expansion report and a wealth of other data did little to alter assumptions that the Central bank would likely keep raising interest rates regardless of whether the economy slows down. This implies that portfolios will experience more losses during the first quarter of 2023. I'm currently at a crossroads deciding whether to exchange my $250k security/stock portfolio; how might the continuous market volatility work to my advantage?

[@MarcelPhilips]

Concentrate on two main objectives. First and foremost, keep yourself safe by knowing when to sell stocks to reduce losses and maximize gains. Second, prepare yourself to gain from a market turnaround. I advise you to seek the advice of a representative or financial counselor

[@MarcusFred-wn3iv]

@@MarcelPhilips In fact, ever since Coronavirus, I've been in regular communication with financial examiners. Nowadays, buying moving stocks is quite easy; the trick is knowing when to buy and when to sell. The section and leave orders for my portfolio are made by my counsel. accumulated more than $550,000 from a $150,000 savings that was initially stale.

[@MarcelPhilips]

@@MarcusFred-wn3iv Please provide the information for your investment advisor here. I really need it now.

[@MarcusFred-wn3iv]

@@MarcelPhilips She is MARTHA ALONSO HARA, my consultant. Since then, she has devoted section and leave attention to safeguards that I have been keeping an eye out for. You can locate information about the chief online, on the off chance that you're interested. I made no regrets about substantially adhering to their exchange strategy.

[@MarcelPhilips]

@@MarcusFred-wn3iv Thank you, Going through her profile on her webpage out of curiosity, and surprisingly she seems proficient. I appreciate this.

[@qflexmoves]

Thank you, kind sir. This is such a simple explanation and easy to understand. I'm back in school pursuing an engineering degree and I always like to understand the WHY behind the formulas provided. You've earned another subscriber. Have a blessed day.

[@kshitishp3662]

Sir. I think you are one of the best mathematics teachers on KZbin.....I recommended your videos to all my friends and am waiting to see your channel grow...I'm a High school student from India.... thanks a lot sir for helping me and others ...I think you deserve "atleast" a million subscribers in my opinion

[@DrTrefor]

Thanks a tonne!

[@yulinliu850]

A wonderful series of videos to look forward to!

[@itsmissy_]

Thank you for this video! Learned these things in math and didn't understand the different uses and situations for them!

[@L-Dyne]

THANKKK YOUUUUUU SO MUCHHHHHH. THIS HELPS ME UNDERSTAND THE CONCEPT OF INTEREST MUCH BETTER

[@RayyanSins]

I'm doing Class 10 AP Mathematics, and you're my go to for revision and recaps, thank you for the outstanding time, effort and thought you put in these videos to make it easier for our understanding!

[@Gabriel-qm9fj]

Your videos are incredible you are loud and clear and your explanations are on point

[@samk1i287]

Helped me a lot! Thanks!

[@SystemsProjectEngineer]

Outstanding job on the explanations.

[@soniaferrer-ponce]

Awesome! Awesome! Awesome! Loved the explanation but your passion is key!

[@drdre4334]

That's a great idea! Thanks!

[@deratu5517]

Well, I liked the way you explained the topic and I hope to see more of that. Nice one!

[@DrTrefor]

Thanks, will do!

[@pregodio0707]

That's some awesome stuff... wish people know more of this.....

[@aadrikasharma4657]

THANK YOU, this is such a GREAT video. Really appreciate all that you do here:)

[@DrTrefor]

You are so welcome!

[@orlandoanderson6040]

That was really a great explanation. Thank you.

[@elonak1529]

Your channel is awesome :) Love your calc videos and this idea!

[@DrTrefor]

Thank you!

[@minma02262]

I love this!

[@nelsonberm3910]

Great video thank you!

[@gustavovizcarra28]

Your courses are great and very helpful... just... amazing.

[@DrTrefor]

Thanks so much

[@harkharajbharali808]

Keep making videos sir. You are best. Love from india

[@andreschancach6438]

I love your videos, you have a unique way of explaining them!

[@DrTrefor]

Thank you!!

[@kathy9124]

@@DrTrefor - yes, I really like your approach! I wish I could have had you as a math teacher when I was younger.

[@SLCKaled]

great video!!! I love that I can apply this to learning about loans

[@Ali-bc7rk]

I enjoyed it, thanks.

[@malakalghamdi8815]

i wish if i can add 1000 likes you deserve it, explained exactly what need thank youuuuuuuuu

[@Bizworld90]

Thank you so much very clear

[@zeinaaiman8567]

Thank you so muchhh ♥️

[@eyalschnider]

thank you profesor.

[@clockfixer5049]

Should we expect duration, convexity, portfolio risk? Great stuff this first video!

[@DrTrefor]

Thanks! I'm not 100% where this will look like down the road, basically the plan is to start at the basics and build up. I do think we will get to more advanced concepts like portolio risk but we shall see:D

[@Agent29416]

@@DrTrefor any plans of doing game theory then?

[@elgatito00]

Woah this is great!😮💘

[@DrTrefor]

Thank you!!

[@idopaz1659]

Amazing as always, this is such an important subject to focus on. As a more mathematics oriented watcher, I was wondering if you are going to make videos on more complex subjects such as tensors, abstract algebra or curvilinear coordinates. Either way, keep on the great work!

[@DrTrefor]

A tensor video is definitely on the list. I’ve debated abstract algebra, but this is (often, not always) a little less geocentric so I’m not sure if I can add so much they way my animations help vector calculus for instances

[@billybobjocrabb7095]

thanks my dude

[@-Joseph]

This is great!

[@DrTrefor]

Thank you!!

[@yanivavraham3772]

Thank you!!! Please give us more episodes from the same topic!! "Math money"

[@SALIMAMUTAYA]

Good explanation ❤❤❤

[@hamzaouladbenayad3053]

very Wonderful ❤❤❤❤....

[@veerakumarsundaram]

Great job 👏 🤝

[@DrTrefor]

Thank you!

[@johntotokenyi5706]

Best Dr

[@JJ-eb4tx]

Great Video! I hope the next video will be about credit risk theory.

[@DrTrefor]

That’s a great one actually!

[@hetkapatel5111]

Thankyou

[@thatomofolo452]

Compound interest is the best 💪💪💪

[@shyamdas6231]

Anyone who wants to know the origin story of the number e, should check out this video. Thank you , sir.

[@Surfsailwaves]

Very nice explanation, thanks. But I believe you need to have the factor P on the RHS in the final line…otherwise the initial amount would not matter at all.

[@Surfsailwaves]

And I then saw your pinned comment! Really this was a superbly clear lesson…

[@mihirrao10]

Brilliant as always! I just wanted to ask that whether we can expect a STATs course on this channel since that is the only one that remains out of the core Math requirements of Computer Science? Thank you.

[@DrTrefor]

haha, the most common request lol! Ok full disclosure: I am NOT a statistician so I could do a bad job tomorrow, but to do a really good job I need to improve a good amount first. So it will happen, but neither of my two planned series for his summer is stats:D

[@wooddog007]

the verb is actually "lend" not "loan" ... loan is a noun ... the verb is "to lend" ... "if I lend you $100" ... not "loan you $100"

[@michaelkorrek7856]

Ok so now an english professor...go to california or deep south but you "aint" Taking that word away

[@Molaleni]

I understand everything you said in the video, it makes sense. However, what confuses me is that I was always under the impression that the formula for simple interest was this: i = P•r•t. I still see similarities to A = (1 + tr), but I’m wondering when is it appropriate to either.

[@zerilioner639]

Hi, I have one math question: Determine the equations of two lines that pass through the point (-1,-3) and the tagent to the graph of y=x^2+1.

[@simonribas4625]

Ah yes, next the black scholes model please!

[@DrTrefor]

Probably not next, but yea this is exactly the type of thing I’d love to get into

[@simonribas4625]

@@DrTrefor hahah! I was only joking as that would be a leap.. but I love to see the mathematics in finance and appreciate your videos! Very easy to think about these formulas in a way that makes actual sense.

[@simonribas4625]

@@DrTrefor and to clarify... not a leap for you but from this topic lol!

[@michaelkorrek7856]

Do yall men schools or scholes..not being smartass just asking

[@shubhamsatyaprakash54]

Amazing as always Dr. Trefor, may I suggest Stock and shres, dividend, market value, brokerage for the upcoming video on Money Math series....Thank you

[@DrTrefor]

Definitely want to hit some of those topics

[@jpalreis]

Great video! One thing that always bothered me is the way that interest is calculated for periods different than a year (not about your video, but the concept itself): the time is adjusted proportionally to the quantity of periods: nt; the ratio is proportionally adjusted to the inverse of the quantity of periods: r/n. Here is the problem: the time is adjusted while being an exponent, while the growth factor (not the interest rate) should be adjusted by inverse of the quantity of periods as an exponent, becoming a root: (1 + r )^t = [ (1 + r)^(1/n) ]^(nt), which (1 + r)^(1/n) would be a new growth factor, having a different interest rate than r/n, say R, compounded for each one nth of a year, as follows: (1 + R) = (1 + r)^(1/n), (1 + R)^n = (1 + r), (1 + nR + C(n,2)*R^2 + ... + C(n - 2,n)*R^(n - 2) + n*R^(n-1) + R^n) = (1 + r); Dismissing all the powers of R greater than one, it is possible to conclude: (1 + r) = (1 + nR + … + R^n) > (1 + nR), since R > 0. So: 1 + nR < 1 + r, which yields R < r/n. Now, using the standard adjustment, r/n would be effectively greater than it should be to make both situations equivalent: compounding once a year or n times a year. So, the formulas would not be equivalent. Instead, it would be a way to increase the actual annual interest without explicit saying so. This is also true for the continuous case since e^r - 1 is greater than r (r > 0 which can be verified by Taylor expansion on e^r - 1). Also, as expected for being the limit when n goes to infinity, the difference between the adjusted rate (e^r-1) and the actual rate r will increase as r gets bigger. Another way to visualize the difference would be to focus that the factor e^r has an exponential graph while the standard adjustment factor (1 + r) has a line as its graph and is also exactly tangent to e^r at r = 0. Together with the second derivative of e^r being always positive, this will yield that e^r > 1 + r, for all real r. Does this make sense? or am I missing something?

[@michaelkorrek7856]

Not to me ive been out of scool for 50 yrs..lved math but omg

[@firstname4337]

this video was interesting

[@DrTrefor]

Glad you enjoyed!

[@bottlecap6169]

I'll definitely be watching this series, but I was wondering, will you still be doing a Summer course on Game Theory like you mentioned in one of your previous videos?

[@DrTrefor]

Yup. Things got a little delayed as I was working out a sponsor for the game theory series but the plan is alternating game theory and financial math as “series” and then random one off videos in between. Should get us most of the way through the summer:D

[@bottlecap6169]

@@DrTrefor Awesome, I'm looking forward to it!

[@Werewolf0216]

In continuous interest, what is "e"? It would have been nice to have an example of this.

[@user-pu6qx9eb4r]

Maybe present value, future value, EMI calculation could follow after this.

[@DrTrefor]

Yup, definitely touching on those either next video or one after:)

[@thomasc4777]

Hey Doc., very informative. As a senior citizen, I'm always focused on the APY for a savings yield. However, if the APY is 5%, does it really matter how often the interest is compounded? I ask because the yield on the annual investment can never exceed the 5%. That is, if I invest $10,000 with a 5% APY, the amount at the end of the year cannot exceed $10,500. That's why how frequently the interest is compounded can be misleading without always having your eye on the APY as the most important factor. Am I looking at this correctly? Thank you.

[@Hassan_MM.]

Pls.Through more light on (e).Is always base of Exponential function

[@jimmyt_1988]

It was fun to try and work out the next equation at each stage. It was also good because, before you gave the next equation, I was taking a guess at what you meant by compound (because I'm an idiot and don't know what words are... what r dis?) and it made me try all sorts of funky equations - one which was interesting was me doing a P * { sum from 0 to n of pn-1 * r } to get a percentage of each newly adjusted total from the last month.. obviously wrong, but cool nonetheless. Trying to figure out what a reasonable answer should be from it was also a good challenge... then after playing the video again, I was like "ahhh, cool... But also, really cool I got to try other stuff out too". Really well laid out video... I thoroughly enjoyed it, even though it's about money hehehe.

[@vnghnfghn7881]

pls Help me with this : When to use the equivalent interest rate as the discount rate?

[@lisarichter203]

I appreciated the video, but may be the only viewer who wished that e was defined. I understand that it substitutes for (1+r/n) under continuous compounding, but what is it called in a finance context (apart from being called an exponential and continuous function)?

[@taetae145]

Sir, can you please make videos introducing the basics of MATLAB.

[@DrTrefor]

I might do that actually, it's a good idea

[@feynstein1004]

14:19 Shouldn't that equation be A = P*e^(rt)? P is a constant and independent of the limit, so it wouldn't be a part of the exponential function. If P weren't a part of the equation, that would mean that the interest would be the same no matter what the principal was 😋Also, it's spelled "principal", not "principle", I believe.

[@DrTrefor]

Indeed! Yes sadly I didn’t notice until after, but it IS a pinned comment at least. Thanks for noticing!

[@feynstein1004]

@@DrTrefor And ironically, I didn't notice the pinned comment until after I'd made my comment 😅 So I guess we're even 😂

[@Loots1]

Will this series go deep into mathematical finance? If you want me to be more specific I can be

[@DrTrefor]

It sort of depends. Going to start simple and build up quickly. How far we get exactly will depend

[@Loots1]

@@DrTrefor thanks for the reply! Keep up the good work it helps a lot :)

[@michaelkorrek7856]

Question..i owe 4000 on my credit card with 8.9% apr. Im only paying 125 a month which minimum is 100..how much more can i pay to make substantial difference..i only have ssi income

[@vidya014]

Dr. The direction of value investing is actually aiming for "compounding interest". Compounding interest is actually talking about compounding dividend. A growth stock which consistently pay dividends, consists of “Intrinsic Value Compounding” and “Dividend Compounding”. Rather than saying “Intrinsic Value Compounding” is being invented, i would say that “Intrinsic Value Compounding” is rather a discovery of a buried compounding inherited in a consistently growing stock. Nobody knows there is so called “intrinsic value compouding” except Buffett, Munger and Li Lu. I am very sure about this argument. If you want to have a breakthrough in the new value investing, i suggest you start to do research on “Intrinsic Value Compounding". Logic and reasoning are utmost important. Hope you found the way to reveal the right formula of “Intrinsic Value Compounding”. The impact power magnitude of “Intrinsic Value Compouding” is very much stronger than the widely spoken “Compounding Interest” aka “Dividend Compounding”. Cheers

[@michaelkorrek7856]

How can one brain hold so much informationand have a great recall..my rcall is at about 10%

[@Eduardo-cr8ri]

Can you do black scholes? :)

[@michaelkorrek7856]

I thought those were outlawed in 60s and70s

[@IdeaStealer]

Where can i get the calculator in 2023?

[@sodiumhyposulfite5902]

Financial Mathematics POG

[@lottabedhead]

hi afif

[@mouradelcadi]

make the poor poorer and make the rich richer

[@franklingps2821]

Confusing explanation of a simple topic.

[@Yahaya-w8l]

U are sweet

[@wyatt1153]

This guy is in the weeds. Very poorly explained.

[@mattkriese7170]

This was an awesome breakdown. It's even better that it was done in Canadian dollars so that I could comprehend 🦫🇨🇦😉