Hi there, I'm Josh! JK Math is an educational resource I've created to help students learn math better through simple and clear tutorials. I hope you find them to be helpful!
Courses Covered:
→ Calculus 1
→ Calculus 2
→ Calculus 3 (Currently in Production)
→ Financial Mathematics
Need to contact me directly? Best way to get in touch is by emailing me at the address found here in my bio (on KZread desktop only)
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Пікірлер
Is there an easy way to calculate total principal paid after time 10? or would you have to individually calculate every time period and add them up.
For all the formulas related to calculating total interest/principal I would recommend checking out my new Unit 3 review video (it's in my FM playlist). In the beginning of the video I review the formulas for amortization, including some I didn't talk about in the lesson and examples video for amortization. In general, the total amount of principal for the entire loan is the amount of the loan. So, if you want to find the total principal paid up to a certain time, you can take the amount of the loan L and subtract out the outstanding balance at that time. You can certainly add up P1, P2, and so on to P10, but as you implied, that would be a bit time consuming.
Isn't it more intuitive for the formulas to say BV(t) = BV (t-1) - PR(t) INSTEAD of BV(t+1) = BV(t) - PR (t+1). If I ask you for the book value at time 2. It seems more intuitive to use the first formula rather than the second.
That is a matter of opinion. Both formulas are technically the same, you are just changing how you refer to each time period. The reason they are given as (t+1) is because of the order in which you would usually fill out an amortization schedule. Usually you know BV(0) to start, as it would be the price of the bond (or original amount of the loan), so then it makes sense that from there you would find I(1), which if t=0, then t+1 is 1. There is no I(0) or PR(0), so that's why we go to t+1. So you calculate I(1) then you can find PR(1) by subtracting it from the payment/coupon amount. Then you can find BV(1) which would be BV(t+1) by taking the original BV(0) or BV(t) and subtracting PR(1) which is PR(t+1). So from my point of view, using the t+1 is more intuitive, but again, that is a matter of opinion. The notation is not necessarily the most important thing here, doing the calculations correctly is the ultimate goal. However you like to go about the notation is fine, as long as you understand the calculations.
Hi thanks for making it so simple to my understanding I realize you only use the graphical method to explain bounding is there any other way without the use of graph
I suppose you could determine the bounding without drawing a graph, but I believe drawing the graph helps give you a visual confirmation of the bounding. You could certainly just write out a couple terms for the sequence and see what is happening to their values, but determining if they are bounded above/below is then a little more about using your intuition rather than looking at a graph which visually supports your conclusions. Also, depending on how you are being graded in your own course, it may be necessary to draw a graph in order to prove your answer or "show your work." So my recommendation is to use a graph, but if you are pressed for time I can see how you might want to skip it, if you are good at using intuition to determine bounding. Hope this helps!
Why isn't it (1+r^n) ÷ (1-r)? 3:35
The exponent needs to be n+1 because of the way the terms are structured in this geometric series. Notice that the first term is for n=0, so there are a total of n+1 terms when you include the n=0 term. If we were starting at n=1, then it would just be r^n as there would be n terms. Does that make sense? Let me know if this helps!
@@JKMathcan you do its derivation pls
@@farhaankhodabaccus3466 This FM course assumes that you have a background in calculus, because you will need to use calculus for certain topics, so that is why I do not show the derivation of the geometric sum formula, it is something that you learn in calculus. Geometric sums are not the focus or purpose of this video, it is about calculating the future value of annuities. With that being said, I do derive the formula for the sum of a geometric series in Lesson 22 of my Calculus 2 series, which you can watch here: kzread.info/dash/bejne/kWafsJNup8y8qZs.html Hope this helps!
@@JKMaththank you for your unflinching support ... god bless
this channel is so underrated .you explain very clearly
You became my next favourite Math KZread/Teacher after "The Organic Chemistry Tutor"!❤❤❤
4:18 why isn't it y/2 tends to 0 under lim?
In that example, the point I was trying to make is that it doesn't what variable expression you are working with, if you have the limit as some variable approaches 0 of sin of that same variable divided by that variable, then the limit is 1. When I let 2x=y, we are just replacing that in the function for the limit, and then looking at the limit for the new variable y. We don't replace x with y/2 under the limit, we are simply looking at the limit as y approaches 0 for the function where we change 2x to y. Does this make sense? I can see where the confusion may have been, so I hope this clears it up. Let me know!
Fantastic !
This is a question on average radius r at 4:30. Normally r is just equal to x. Instead of x, can we just use (a+b)/2 which is the actual average radius? Conceptually, we can take the area bounded by f(x) from a to b multiplied by the thickness 2pi(r) where r = (a+b)/2.
No, the radius always needs to be defined in terms of x, it will not be constant. I see why you would think it could be (a+b)/2, but remember that in that diagram I drew, that was just ONE cylinder that is representative of many cylinders we are using to find the volume using the shell method. So each cylinder will have a different average radius. That's why we need to use x, as the average radius of each cylinder will be dependent on where those cylinders are located along the x-axis. You can test this out with the example problems in this video, if you change the radius from x to (a+b)/2 you will get a completely different answer, and it will be an incorrect answer. Hope this helps!
@@JKMath Thanks for the reply.
Would it be correct if for finding f{2,3} instead of using (1+s2)^2(1+f{2,3}) we use (1+s1)(1+f{1,2})(1+f{2,3})?
Yes! That would also be correct. It's definitely unusual, but it could make sense to do it that way if you happen to know that other forward rate in a specific problem.
This is the concept of "write-down" of premium and "write-up" of discount correct?
I'm not familiar with that terminology, I suppose that may be the case but can't confirm either way. My expertise with these videos lies more in the math/solving the problems, not necessarily the complexities of the financial concepts themselves.
Why would it be that in example 1, P(t) is less than P(0) but then in example 2 P(t) is greater than P(0).
Those differences have to do with the fact that the bond in example 1 would be bought at a premium/greater than par value (because r > j), and the bond in example 2 would be bought at a discount/less than par value (because r < j). Depending whether r or j are bigger will affect how much is accumulated for the fractional amount of time, and how much is subtracted for the fractional coupon. Sometimes the fractional coupon is greater than the amount of accumulation and vice versa.
I love your explanation of concepts so much! One thing I wanted to ask, do you have or plan on doing any videos about differential equations? I know thats an entirely different math class but my Calculus II professor is introducing them and going over separable differential equations. I would love to hear your explanation of these!
Thank you for the kind feedback! I really appreciate it. I have no differential equations videos right now, but I do have plans to cover it one day. However, that is most likely very far in the future. My goal is to one day cover all major math courses, but I am only one person doing all the writing, recording, and editing, so it will take a lot of time. Right now I'm finishing up some FM videos, and then I plan to complete my Calc 3 series before starting any new courses. Hope you can understand! :)
@@JKMath I completely understand! I love, respect and appreciate all the work you put into your videos!
For the 3rd problem, would it be correct if upon calculating the price of the bond using 50 as amount of coupons for a total of 40 coupons with the yield rate of 0.07 convertible semiannually and finding it to be 1351 to say it’s premium (1351>1000) so we calculate the price at the earliest date possible which is at t = 28?
Usually that would be the case, but in this problem we are not told the face value/par value. We do not know for sure if it is 1000, we can guess that it is based on the given numbers, but we still can't assume that it is. So, we also can't make the assumption that the bond is bought at a premium because we don't know what F is. Putting that aside, even with your assumption of F=1000 (which we can't do) you still had to calculate both prices (for n=28 and n=40) which doesn't change the work needed to find the answer to the problem. You still had to calculate 2 prices and compare them like I did in the video. Hope this helps!
@@JKMath so basically if we’re never given a face value - even if we’re still given a redemption value- we can never determine whether it’s bought at premium or discount? Also if it was given that it has face value of 1000 why do we need to compare earliest date against maturity one? Is it because of the call premium of 125?
The way I understand it, yes. When F is unknown, a redemption value C, while usually close to the face amount, is not an indicator of discount/premium on its own unless the problem states otherwise. And what I meant by still needing to compare the prices if you assumed F=1000, notice that you calculated the price using n=40 to see if it was a premium. You wouldn't have to do this, I was just saying that in your explanation you did, so the work was very similar. If we knew that F=1000, then from that we could find the coupon rate since 50=Fr, r would be .05, so you could compare that to the yield rate to determine premium/discount based on that. There would be no need to calculate 2 prices in that case.
@@JKMath thank you very much it’s all become clear now 🙏🏻
Awesome, glad I could help! :)
holy shit, this is a way shorter explaination for the formula than the professor leonard's one. thanks
Bro your video is the exact video I was looking for. I’m so grateful to find your video
when will you bring p exam videos 😢
One day I will cover exam P topics through a series on probability & statistics, but It will be a while. I am only one person, so I have to focus on one thing at a time. After finishing the review videos for FM I will be completing my Calc 3 series, then I may consider a new course such as probability. I do all the lesson writing, video recording, and editing by myself, so it takes time to produce new videos. Hope you can understand!
@@JKMath Yes I can and I'm eternally grateful for all of your lessons which are so well done and executed! You're definitely doing so much :D
I dont understand why are you taking m as 1/2 in the first question when the interest is compounded bi-yearly
In that problem, interest is being generated every two years. The period cycle is a 2 year period, not a period of twice per year. In other words, this is not a semiannual interest rate, it is a 2 year interest rate. The value of m represents the number of times the rate would occur in a year, so since the rate we are working with is a 2 year rate, only half of it would occur in 1 year. Hence why m=1/2. It is not m=2 because that would mean semiannual or twice in one year. Does this help? Let me know!
This channel is severely underrated. Your explanations are so good and never too repetitive or superfluous, with a good number of examples to help practice what you teach.
Very good, I am impressed. I admire your work, keep goint bro. You really making a good stuff. Thanks to people like, it is easier for us to understand very hard concepts)
Thank you, I appreciate the kind feedback :) Feel free to share these videos with others!
Hey Josh, thanks to your videos I am finally able to pass the FM sample exams. I hope for the best in the real exam in a few weeks. Out of curiousity do you have any videos doing the SOA Probability exam that comes up next? Or do you have any recommendations of where to find similar resources on that one that you provided for FM.
That's awesome, glad to hear that! I wish you the best on taking the real exam, you've got this! At this moment in time, I don't have any videos on Prob & Stat (or Exam P topics), but it is definitely something I will cover in the future at some point. I would recommend you check out the channel AnalystPrep, they have a playlist on Exam P. I'm not sure if it includes everything you need to know for the exam, but there is a lot there to at least get you started and build a good understanding of the main topics. Also, the society of actuaries (SOA) website does provide a syllabus for the exam that includes recommended textbooks if that's something you are looking for as well.
@@JKMath I think one thing not covered in your videos is first order calculations using Maculay and Modified Duration. Maybe it's new to the test?
Yes, that is true right now, but it won't be for long! Crazy timing on this comment, as I'm currently working on a lesson and examples videos for that topic right now haha. Should be out in a week or two, so stay tuned!
Hi JK. I really like your content. I was wondering, what whiteboard software do you use?
Thanks! I use an app called Goodnotes for all my videos.
You are such a kind person🥰🥰. Thank you so much for making these videos. Truly Appreciate it🙏
You're very welcome! :)
Does it have replay bottom?
Am I missing something. If the bank account only had 100 dollars on January 1st, and the rate of return is 10%, wouldn't it have 105 on July 1st before any additional withdrawls?
Not necessarily. The dollar weighted rate of return is a rate that we calculate as a measure for an account at the end of the year, after the year has already occurred. It is not necessarily the rate that would have actually generated the interest for the account. The same goes for the time-weighted rate of return. These are rates that we are calculating after the fact to measure growth in an account in different ways. Further details about what those rates actually tell us about the account is beyond the scope of what my videos are intended to teach. But the bottom line is that the way I understand it, the DRR and TRR are not the rates used to generate interest in the accounts featured in these problems, rather they are separate measures for those accounts that can be calculated after a year of account activity ends. Hope this helps!
@@JKMath Yeah it does, thanks!
youre actually the goat
You're saving lives😭❤️
Your videos are amazing! I will recommend these to all my friends
Thank you! I appreciate the support :)
I had watched a couple of videos on this, your explanation is the best so far and easier to understand. Thank you for making this much easier for students!
You're welcome! Glad to help :)
i might be remembering wrong/mistaken but when you do U sub dont you need to update the bounds of the integral?
Only if you don’t change back into terms of the original variable. If you are referring to example 2 in the video, notice that after I integrate in terms of u I substitute back what u was set equal to (2y). By doing that there is no need to change the bounds of integration. However, you could also leave the integral in terms of u, but then you would have to update the bounds by plugging in the values into what you set u equal to. In other words, there’s two different ways to go about it, I chose to go back into terms of y but you could do it differently, you’ll get the same answer regardless. Hope this helps!
I think there is a mistake in example 3. I am getting 7.95%. I used a different method but checked with your method and it doesn't make any difference. Multiplying 0.0066227 multiplied by 12 gives 0.0795.
That’s the same answer I give in the video except rounded to 4 decimal places. I wrote .07947, but that can be rounded up to .0795. My 9 looks a bit like a 7 I guess, that’s my bad, but I do verbally say the digits correctly in the video.
@@JKMath Ah my bad. I read it as a 7. I did the exercise on my own and only checked the final answer, so I didn't hear you. Sorry about that.
No worries! Definitely not the best 9 I’ve ever written haha. Can definitely see how it could be misread.
I literally love these videos so much. My professor did such a bad job explaining this in class today and I was so lost! But you do such a great job and provide such a detailed explanation, literally anyone could understand it! Thank you so much!
You are very welcome! Glad I could help, thank you for sharing this :)
Hey @JKMath , it's a small request, I'd really appreciate if you could do some videos for Sinking Funds too. Your videos are really comprehensive and easily understandable :)
Thanks for the suggestion! I will add it to my list of topics for potential "one-off" FM videos to make one day, similar to the Drop vs Balloon payment video in my FM playlist. I appreciate the kind feedback!
you're so underrated! i've been watching your videos regarding series and they're so helpful. thank you so much
You're very welcome! Glad the series videos have been able to help you, I know how overwhelming series can be when first learning about them. If you ever have any questions please feel free to let me know! :)
Thank you sooo muchhhhh 🙏🥹
You're welcome! :)
Thank you for teaching me MacDonalds duration
You are very good in explaining. I'm not sure why you don't have more subscribers.
Thank you, I appreciate that! The channel is still relatively new, so it will take time to grow, but I'm committed to making more and more tutorial videos regardless. Feel free to spread the word and share these videos with others! :)
Hi, I love your content and the way you teach but I would appreciate if you teach how to use that in Financial calculator as well as this formula will become so much easier for students to compute the results . Thank you.
Thank you! Glad you like the videos. In my main lesson and examples videos I purposely only focused on the math side of things and left using the financial calculator for a different video, which you can find in my FM playlist. I don’t talk about durations explicitly in that video, however you can calculate them with the help of the cashflows function in the CF button on the BAII plus. You can calculate the NPV for the cash flows for the denominator of the MacD and then do the same thing but multiply each cash flow by the appropriate time value to calculate the NPV for the numerator. Store each of those values in the calculator then recall and divide the numerator by the denominator and there’s the MacD. To get to the ModD then you could multiply by 1/(1+i). Hope this helps!
@@JKMath Thank you for your guidance and looking forward to learn more.
extremly good
講解得好清楚 讚 !
Taking my first actuary exam in a month and it's been so difficult to find free high-quality resources out there to study. Thank you for your contribution! These videos have helped me tremendously.
You are very welcome! Best wishes on your studying and on the exam! If you ever have any questions, please don’t hesitate to let me know :)
What is the difference between clear term and clear work? Which should we use?
Good question, I don't exactly make that clear in the video and I apologize for that. CLR TVM is for clearing out values dealing with the TVM buttons such as N, I/Y, PV, PMT, and FV. On the other hand, CLR WORK is for clearing out other menus you may be working in such as the cashflows menu in CF, and the interest rate conversion menu in ICONV. Hope this helps!
Thanks for the effort you put in! Your practice problems & guided solutions are helping me get better :)
You're very welcome! Glad to know the videos are able to help you :)
Thanks for making it easy ..
You're welcome! Glad I could help :)
best video ever:) Hard to find good info about this!
I don't understand why exact matching isn't "immunized". I understand the concept mathematically, but what could possibly happen that would result in the net present value being less than zero? I feel like the third condition should be that the concavity is greater than or equal to zero. Just from a pragmatic standpoint.
The way I understand it, exact matching is technically still a form of "immunization", it just is not Redington immunized or fully immunized. The point I was trying to make in the video is that by pure mathematical definitions, exact matching doesn't meet the requirements to be Redington immunization or full immunization. It may very well still be a viable choice to protect your assets and liabilities, if you can achieve exact matching (which is probably unrealistic), but you can't say it classifies as Redington or full immunization based on their definitions. Does that make sense?
@@JKMath Yes, I fully agree it doesn't meet the mathematical definition. However, it seems that the mathematical definition doesn't match the colloquial use of "immunization". It can easily be fixed by saying that the second derivative must be greater than or equal to zero rather than just greater than zero. I am new to the field of finance. My degree is in physics, so my perspective is a bit different.
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Bro you make fire videos please keep this up!!
Thank you! Glad you enjoy the videos. Feel free to share them with others! :)
First of all: THANK YOU for those videos!! They're a blessing for my MBA start atm. One question regarding problem 2 - why do we take 5 periods of interest (1.07)^5 instead of 4 periods, meaning (1.07)^4? In the first part of the problem, we calculate an annuity immediate - so Chuck ends his deposits at the END of year 10. Inbetween year 10 and 15, he‘s earning interest. However, since he starts his withdrawals at the BEGINNING of year 15 (annuity due), I figured he would be earning interest up until the END of year 14 (accordingly, 1.07^4) and not up until the end of year 15. Could you explain that to me? :)
You are very welcome! Glad the videos are able to help you :) Regarding your question for problem 3 involving Chuck, I think drawing a timeline for this scenario would help you visualize/understand why we accumulate interest for 5 years instead of 4. Unfortunately I can't draw a timeline in a KZread comment, but I'll try my best to explain it with words. To start, you are correct, we calculate the future value of an annuity-immediate to begin, so that will be valued at the time of the final payment for that annuity. In this case that would be at t=40 for the last quarterly payment in 10 years, but you can think of t=40 as the same thing as year 10. Note that every payment is made at time t=1, then t=2, ... , up to t=40. So the last period takes place between t=39 and t=40. (Remember, the first period is from t=0 to t=1, the first "period" does not start at t=1, so this may be where you are getting confused with the beginning of year 10 vs the end of year 10. If we were measuring t in years, the 10th year is from t=9 to t=10). So then, from year 10 to the beginning of year 15, nothing is happening except interest is being generated. Again, you are correct that the second annuity is an annuity-due, so the payments are made at the beginning of each period. Regardless, there is still 5 years between the end of the annuity-immediate and the beginning of the annuity-due. You count all of years 10, 11, 12, 13, and 14, which takes you to the beginning of year 15. That is a total of 5 years, so we need to use (1.07)^5. Does this make sense? Again, this would be more easily explained with an actual drawing of a timeline (in hindsight I wish I drew one in the video), but I hope this explanation helps clear things up. In fact, I would recommend you try and draw out a timeline yourself, and I think you will see what I am talking about.
@@JKMath Hey, I appreciate you taking the time to answer so quickly and thoroughly! Your guess is correct: I assumed, the last payment for the annuity immediate would be at the end of year 10 and NOT in the period between t=9 to t=10 (talking years here). After drawing a timeline while following your explanation, the five periods of interest make sense to me. Thank you!!
@@a.bonkowski You're welcome! Glad I could help clear that up for you.