Relationship between bond prices and interest rates | Finance & Capital Markets | Khan Academy

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  • เผยแพร่เมื่อ 27 ก.ย. 2013
  • Courses on Khan Academy are always 100% free. Start practicing-and saving your progress-now: www.khanacademy.org/economics...
    Why bond prices move inversely to changes in interest rate. Created by Sal Khan.
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    Finance and capital markets on Khan Academy: Both corporations and governments can borrow money by selling bonds. This tutorial explains how this works and how bond prices relate to interest rates. In general, understanding this not only helps you with your own investing, but gives you a lens on the entire global economy.
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ความคิดเห็น • 549

  • @Edwin-kv1eu
    @Edwin-kv1eu 3 ปีที่แล้ว +642

    Kahn helped me back in high school; now he’s helping me navigate the markets. Can’t get rid of this guy.

    • @jochem2710
      @jochem2710 3 ปีที่แล้ว +3

      Haha, great comment!

    • @salonibansal6043
      @salonibansal6043 2 ปีที่แล้ว +6

      Sameeeee. A big help in navigating and understanding the market concepts which I should have learned in school.

    • @PunmasterSTP
      @PunmasterSTP 2 ปีที่แล้ว +1

      Hey I'm just curious, how has investing been going?

    • @A2Cap
      @A2Cap 2 ปีที่แล้ว +5

      @@PunmasterSTP horrible lmao nassy falling 3% everyday

    • @PunmasterSTP
      @PunmasterSTP 2 ปีที่แล้ว +2

      @@A2Cap By nassy do you mean Nasdaq? Yeah I agree things might not be the best right now. But just like you can sail into the wind, I would suppose that bear markets can present their own opportunities…

  • @CRMills
    @CRMills ปีที่แล้ว +126

    Thanks for explaining the SVB issue 9 years ago. Makes sense

    • @WhatsUpWithSheila
      @WhatsUpWithSheila ปีที่แล้ว +8

      Exactly why I came... So I could get a better understanding of what happened❤👍

    • @J0SKXY
      @J0SKXY ปีที่แล้ว +2

      hehe

    • @gilbertmalisa8700
      @gilbertmalisa8700 ปีที่แล้ว +4

      SVB brought me here 😅

  • @Lofibootleg
    @Lofibootleg 4 ปีที่แล้ว +291

    Hi, thank you so much for the video Sal!
    I would just like to add on in case anyone was struggling to make sense of the inverse relationship between interest rates and bond prices like I did. You can think of it as the following scenarios:
    1) If interest rates in general fall, the bond's interest rates become more attractive, so people will bid up the price of the bond.
    2) Likewise, if interest rates rise, people will no longer prefer the lower fixed interest rate paid by a bond, and their price will fall.
    Hope this helps :)

    • @ys5038
      @ys5038 4 ปีที่แล้ว +4

      thanks!

    • @ayaya864
      @ayaya864 4 ปีที่แล้ว +3

      Thank you

    • @AllYouWantAndMore
      @AllYouWantAndMore 4 ปีที่แล้ว +6

      Still don't get it

    • @JasonBong123
      @JasonBong123 4 ปีที่แล้ว +5

      This cleared it up for me. Thanks for the finishing touch kind sir!

    • @vivek447
      @vivek447 4 ปีที่แล้ว +5

      Hi Derek,
      Can you please explain what do you mean by interest rate here?

  • @ttfan3257
    @ttfan3257 3 ปีที่แล้ว +86

    Older bond will trade-at-discount-to-par ( ie older bond price falls) , when interest rates rise (for newer bonds)
    Older bond will trade-at-premium-to-par ( ie older bond price rises) , when interest rates fall (for newer bonds)

    • @kingwoo1900
      @kingwoo1900 2 ปีที่แล้ว +8

      So hypothetically does that means that we should buy bonds when the interest rate is the highest as one can profit from rising bond price when interest rate comes down ?

    • @vlad_shark
      @vlad_shark ปีที่แล้ว

      @@kingwoo1900 Exactly. I think like in this way too

  • @elvismark5172
    @elvismark5172 ปีที่แล้ว +225

    The Federal Reserve's intention to raise interest rates until inflation is under control is still viewed with skepticism by the markets, even if bond yields are rising while stock prices are falling. What is the best approach to profit from the current down market while I'm still considering whether to sell the $401,000 worth of stocks I own?

    • @waynestones
      @waynestones ปีที่แล้ว +4

      If the market has taught me anything, it's that it typically makes a comeback, but I can't seem to focus on the long term, particularly because crucial factors like my retirement and my reserve are having a devastating influence on inflation. As soon as is practical, I need a solution and a data trajectory that I can trust.

    • @alexanderjames3043
      @alexanderjames3043 ปีที่แล้ว +2

      One of the primary reasons I utilize a portfolio coach to oversee my daily investing decisions is that their whole skill set is centered on trading long and short at the same time, utilizing profit-oriented techniques and minimizing risk as a hedge against unforeseen events.

    • @AnthonyHart34
      @AnthonyHart34 ปีที่แล้ว +2

      @@alexanderjames3043 Due to the significant falls, I need advice on how to rebuild my portfolio and develop more successful tactics. Where can I find this teacher?

    • @alexanderjames3043
      @alexanderjames3043 ปีที่แล้ว +1

      @@AnthonyHart34 In fact, I'm not sure whether I'm permitted to say this, but I'd suggest searching for "sharon lee casey" as she gained a lot of attention in 2020. She is both my coach and the manager of my portfolio.

    • @thomaslewis514
      @thomaslewis514 ปีที่แล้ว +1

      @@alexanderjames3043 She has excellent credentials and an outstanding occupation. Hence, I swiftly copied Sharon's whole name and typed it into my browser. I'm curious to discover why she is so busy, and despite the fact that she has unquestionably good credentials, I nevertheless schedule a meeting with her.

  • @realrobh
    @realrobh 6 ปีที่แล้ว +67

    I don't know why I go to school. Why is it so much easier for me to learn from Khan Academy? ?!?!

  • @divyadixit5607
    @divyadixit5607 4 ปีที่แล้ว +9

    He knows everything. Just love Khan Academy

  • @Driving4bangers
    @Driving4bangers 4 ปีที่แล้ว +149

    Is this the smartest guy alive ? How does he know every concept

    • @capgains
      @capgains 4 ปีที่แล้ว +16

      Julian Hilgemann textbooks + genetics + will

    • @ITALIANO0110
      @ITALIANO0110 4 ปีที่แล้ว +1

      @Donald Borum is that hard

    • @DaBestAround
      @DaBestAround 4 ปีที่แล้ว +9

      @@ITALIANO0110 obviously! Extremely difficult. Also, requires a lot of hard work.

    • @ITALIANO0110
      @ITALIANO0110 4 ปีที่แล้ว +1

      @@DaBestAround sorry i meant MIT is it harder than other unis

    • @blankneverlosegaming6374
      @blankneverlosegaming6374 4 ปีที่แล้ว +7

      He was a Portfolio Manager at a hedge fund

  • @bb.edelweiss2199
    @bb.edelweiss2199 4 ปีที่แล้ว +7

    Great teacher, thank you for contributing !

  • @Rendog2
    @Rendog2 3 ปีที่แล้ว +5

    Finally somebody's able to put it in language I understand. Thanks!

  • @PrashantSingh-jj7wr
    @PrashantSingh-jj7wr 4 ปีที่แล้ว +5

    Best explanation available! Thanks a ton!

  • @timjacobs4457
    @timjacobs4457 10 ปีที่แล้ว +19

    Thanks a lot for making this one! Just in time too, got stuck on my financing course and you pop up some videos.

  • @catsmith7084
    @catsmith7084 4 ปีที่แล้ว +21

    Love it ! Finally now i get it ... also watched bonds explained . I have no finance education backgroud but i am now in the mortgage industry and i can definitely benefit from this !

    • @nagasako7
      @nagasako7 4 ปีที่แล้ว +2

      I've slowly invested more into bond funds as central banks slowly cut interest rates since late 2018.

    • @PunmasterSTP
      @PunmasterSTP 2 ปีที่แล้ว

      @@nagasako7 I came across your comment and was just curious. If I might ask, how has your investing been going?

  • @user-mv3jx2qx8r
    @user-mv3jx2qx8r 6 ปีที่แล้ว +2

    amazingly clear explanation. Thanks so much

  • @sharique7133
    @sharique7133 6 ปีที่แล้ว +1

    Thank you very much. This video helped me to get the understanding of Keynes' Speculative demand theory of money.

  • @madras61
    @madras61 7 หลายเดือนก่อน +4

    This was the best video that explains the relationship between Bond and interest rates in a simple term so that one can understand.❤

  • @SejalPatelDrSej
    @SejalPatelDrSej 4 ปีที่แล้ว +221

    now the real question is where can i find that 15% coupon bond lol

    • @saulcohn4844
      @saulcohn4844 4 ปีที่แล้ว +8

      ANGL junk bond etf

    • @dantheman4011
      @dantheman4011 3 ปีที่แล้ว +3

      I would even take 10%

    • @ronniebine1325
      @ronniebine1325 3 ปีที่แล้ว +3

      @@dantheman4011 I would even take 5% given that currently, the interest rate on 30 year US bond is 2.34% & 1.6% on a 10-year bond.

    • @dantheman4011
      @dantheman4011 3 ปีที่แล้ว +7

      @@ronniebine1325 which barely covers inflation.

    • @ronniebine1325
      @ronniebine1325 3 ปีที่แล้ว +5

      @@dantheman4011 Inflation will shoot up soon as theres no chance that FED can reduce it's balance sheet. Gold is on the way to shoot to the moon.

  • @thereversepolarbear
    @thereversepolarbear 10 ปีที่แล้ว +2

    That was really useful thanks. I understood it before, but this was so clear and concrete.

  • @jainamturakhia4688
    @jainamturakhia4688 5 ปีที่แล้ว +7

    Thank you so much! Was really helpful :)

  • @jkxelor1295
    @jkxelor1295 ปีที่แล้ว +2

    Boom! Thanks. I now know more about economics than Janet Yellen!

  • @ir9000
    @ir9000 6 ปีที่แล้ว +2

    I loved your explanation. This made sense to me.

  • @luanateta8431
    @luanateta8431 4 ปีที่แล้ว +3

    Each time I see you, I get light from your eyes.

  • @ethicsessay1120
    @ethicsessay1120 7 ปีที่แล้ว +4

    Very well explained, what could take someone hours in the library to understand, you do that in 13 minutes, thank you very much.

  • @johnholme783
    @johnholme783 ปีที่แล้ว +1

    Quantitive easing makes sense now. Buying bonds increases their value thus bringing down the yield!

  • @johnhess4148
    @johnhess4148 7 หลายเดือนก่อน

    THANK YOU. It took me over a half dozen videos to find this one that makes sense of this insanity. It shows the relationship in real numbers.

  • @rrdawi
    @rrdawi ปีที่แล้ว +1

    Kahn is great and Sal is a good man

  • @justSTUMBLEDupon
    @justSTUMBLEDupon ปีที่แล้ว +1

    This is REALLY applying to what’s happing today. Glad it showed up on my TH-cam feed.

  • @maelmare9280
    @maelmare9280 ปีที่แล้ว +3

    This explanation is a God sent explanation. Well done!

  • @hkinfluenster8713
    @hkinfluenster8713 4 ปีที่แล้ว +4

    Exactly the kind of lesson I was looking for. Thank you.

  • @morwinmanju
    @morwinmanju 10 ปีที่แล้ว

    Sal u are doing a great and appreciable job...

  • @diaojun161
    @diaojun161 3 ปีที่แล้ว

    Thank you so much for the explanation! Really helped me!

  • @jeremyfreetoroam
    @jeremyfreetoroam 6 ปีที่แล้ว +2

    Thanks for the great video and I'm glad you showed the math.

  • @ThinhSan
    @ThinhSan 2 ปีที่แล้ว

    Simple and straightforward explanation, thanks.

  • @jesseonwochei2193
    @jesseonwochei2193 4 ปีที่แล้ว

    Super clear simple explanation in the most profound way.

  • @Noname_7775
    @Noname_7775 3 ปีที่แล้ว

    Perfect explanation! Thank you

  • @ananyaimtiazhussain6816
    @ananyaimtiazhussain6816 3 ปีที่แล้ว

    Wonderful explanation. Thank you so much for this.

  • @zeytee
    @zeytee 2 ปีที่แล้ว

    The best video you can find on TH-cam about the relationship between interest rates and bond prices.

  • @ProfRoofs
    @ProfRoofs 3 ปีที่แล้ว +9

    Who’s here after the drop in the market despite Feds saying interest rates would stay low until 2023?

    • @EmilioCalderonStocks
      @EmilioCalderonStocks 3 ปีที่แล้ว

      LOOOOOOOOOOOOOOOOL

    • @yemisadiq8346
      @yemisadiq8346 2 ปีที่แล้ว

      Fed has a targeted interest rate and this is always in line with inflation. However, Fed cannot control the forces of demand and supply. Hence, real market activities would determine the actual interest rate.

  • @WhatsUpWithSheila
    @WhatsUpWithSheila ปีที่แล้ว +1

    Thank you... I came here because of SVB... And now I understand😁👍

  • @danthemann6565
    @danthemann6565 ปีที่แล้ว +6

    Hands down the best explanation of bond price fluctuation with an excellent mathematical demonstration. Thank you so much.

  • @swagerflava
    @swagerflava 10 ปีที่แล้ว +2

    Thank you so much!!!

  • @chastonantonmatta
    @chastonantonmatta 5 ปีที่แล้ว

    Thanks for the video!

  • @shubhendudeepak8943
    @shubhendudeepak8943 5 ปีที่แล้ว +116

    498K views and 2.2K likes? Why?
    This is one of the simplest ways this particular subject could’ve been explained.

    • @5astelija75
      @5astelija75 4 ปีที่แล้ว +14

      Because no fancy animations, no screaming face and capital letters in thumbnail, no click-bait.

    • @mr.solomun9546
      @mr.solomun9546 4 ปีที่แล้ว +7

      The reason is that most people watch the videos through the KhanAcademy website in an embedded player where the like button and comments are not shown.

    • @TeamHomewardFound
      @TeamHomewardFound 4 ปีที่แล้ว +4

      Because people are LAZYYYY haha I ALWAYS ALWAYSSSS Like a video if I gain value from it. It's the least I can do since I'm not paying for the information. Maybe it's the "TH-cam Creator" in me :)

    • @TeamHomewardFound
      @TeamHomewardFound 4 ปีที่แล้ว +2

      @@5astelija75 RIGHT!!!!
      hahaha

    • @karangupta3670
      @karangupta3670 3 ปีที่แล้ว

      volume is too low

  • @yashugoyal9818
    @yashugoyal9818 3 ปีที่แล้ว +1

    Brilliance man. Really thank you ❤️

  • @theunscriptedcouple5339
    @theunscriptedcouple5339 ปีที่แล้ว +1

    This video is a gem!

  • @qikong7269
    @qikong7269 4 ปีที่แล้ว +2

    Thanks Khan Academy! You saved my finance class :P

  • @orkhanhasanov1922
    @orkhanhasanov1922 4 ปีที่แล้ว

    thank you, perfect!

  • @sagarsapkota2998
    @sagarsapkota2998 10 หลายเดือนก่อน +1

    If i have a teacher like you i never feel finance is difficult from nepal😭😭😭😭🇳🇵🇳🇵🇳🇵

  • @mesferalotaibi7691
    @mesferalotaibi7691 6 ปีที่แล้ว

    thank you so much that was helpful

  • @ponzianomanning3071
    @ponzianomanning3071 3 ปีที่แล้ว

    Thanks Sejal! That tought me in 12min. what would have taken hours to learn in finance textbook research.

  • @torque1523
    @torque1523 2 ปีที่แล้ว +1

    If you're looking for his not math succinct explanation:
    When the interest rate goes up, people expect more return from the bonds which don’t give more because they were issued at a lower interest rate time therefore their price go down (trades at a discount to par).
    When the interest rates goes down, the bonds issued in the higher interest rate time yield above expectations to they go up in value (trading at a premium).

  • @lachlantate2379
    @lachlantate2379 2 ปีที่แล้ว

    Khan academy is actually the goat. I’ve been using Khan for over 5 years now

  • @javier33133
    @javier33133 6 ปีที่แล้ว

    thank you, very clear

  • @happymtonga9427
    @happymtonga9427 ปีที่แล้ว

    Thank you so much Sir for this explanation. You are helping alot of people out here.

  • @samuelspencer5047
    @samuelspencer5047 3 ปีที่แล้ว +4

    Thanks for the video. I believed that with interest rates going down it would want to drive bond holders from bonds and elsewhere due to the low yield, I guess it is true with bonds with variable rate.

  • @tatianazhdanova568
    @tatianazhdanova568 2 ปีที่แล้ว +1

    His writing is so pretty 🤩 every symbol is perfect!

  • @amitkumar-ip6yv
    @amitkumar-ip6yv 6 ปีที่แล้ว

    Sal, awesome video.

  • @donnachandler1758
    @donnachandler1758 ปีที่แล้ว

    This was good. The examples were awesome. Thank you

  • @ssjrosethanos1996
    @ssjrosethanos1996 3 ปีที่แล้ว +2

    My god... After hours and hours of reading my text book and beating myself in the face with my fist I get it. Wish I had watched this video first.

  • @ezilanmu9841
    @ezilanmu9841 4 ปีที่แล้ว

    Finally got that from you !! thanks much

  • @user-ht7gw9ww1c
    @user-ht7gw9ww1c 5 ปีที่แล้ว

    나도 미국에서 수년가 칸아카데미 이용했던 사람으로서 이 칸 선생님응 진짜 존경한다. 미국은 달라... 이분은 공짜 무료 로 이런거 갈키는데 거의 창시자임... 미국이어서 가능 한국에서는 절대 불가능... 대학교육만 봐도 미국대학 근처에 한국처럼 술집 번화가 자체가 생겨날수 없음 그냥 닥치고 아닥하고 공부 ... 기본적으로 전문대 강사라도 해도 미국에서의 교육에대한 자부심이 쩔고 .. 내대학의 경우도 통계교수가 얘기했던게 우리가 미국에서 티칭 스킬이 10위권이다 올해는 14위로 내려갔다 이러면서 점수를 안주려고 하지만 학점에 관계없이 어려워도 이런 교수들 만나 의미있는 교육 받고 공부했다는거에 자부심이 든다. 이 칸 선생님때문에 인도사람들이 더욱 친근해지고 조아졌었징 똑똑합니다 진짜 수학 25구구단이었던가 25진법인가 까지 외우는 나라. 한국은 진짜 달라져야돼 자기 밥그릇만 챙기면 더이상 미래가 없음. 공무원 마니 뽑지 말고 중소기업 마니 뽑아요

  • @IkaikaArnado
    @IkaikaArnado 3 ปีที่แล้ว

    Huh. Good explanation. Definitely found that helpful.

  • @syedahmadmuhajirsyedabdull3188
    @syedahmadmuhajirsyedabdull3188 3 ปีที่แล้ว

    Great Explaination! thank you

  • @dungluu6627
    @dungluu6627 10 ปีที่แล้ว +5

    It's usefull and simple to understand. Thanks.
    Please keep doing lessons like this ;)

  • @makeittrades5750
    @makeittrades5750 8 ปีที่แล้ว

    Great video!

  • @evantipova83
    @evantipova83 3 ปีที่แล้ว

    Thank you, super helpful!

  • @PunmasterSTP
    @PunmasterSTP 2 ปีที่แล้ว

    Bond prices and interest rates? More like "Better and profound information that's great!" Thanks for everything you do Sal.

  • @toothsomeclips1421
    @toothsomeclips1421 2 ปีที่แล้ว

    It helped sir.
    I was stuck in economics for 3 constant days.
    Thanks.

  • @avidintovert5198
    @avidintovert5198 4 ปีที่แล้ว

    Very lucidly described.. thanks.

  • @shambhuneupane3810
    @shambhuneupane3810 7 ปีที่แล้ว +25

    i am happy

    • @incognito7054
      @incognito7054 6 ปีที่แล้ว

      Know what your thinking

    • @eddyvideostar
      @eddyvideostar 6 ปีที่แล้ว

      Shambhu Neupane: Yes, anything which is not too out of my control I am happy with my knowing this is not a chance game like the stock market, or worse, an individual stock. When you touch it, especially a rising market, there is no guarantee that it will do what you desire. Bonds are not a "greedy" vehicle. These are a nexus to the sound rewards it provides.

  • @saabmira
    @saabmira 3 ปีที่แล้ว

    Now that's a saver! Thank you 😘

  • @nikolettamatsur9716
    @nikolettamatsur9716 ปีที่แล้ว

    This is perfect. Thanks!

  • @SAM1057368
    @SAM1057368 6 ปีที่แล้ว +9

    What a brilliant way of explaining the present value of a bond using discounted cash flows, without even introducing it as an NPV of a bond. This inductive reasoning is brilliant.
    PV of Zero Coupon Bonds= Bond's Price/(1+R) where R= Coupon Payments
    PV of Normal Bond= Bond's Coupon payments/ (1+R)^t +Bond's Principal/ (1+R)^t
    t= number of years
    Every time the interest rate, or discount rates, increase, the price of a bond, or its present value decreases.
    We also have to distinguish between:
    Current Yield= Annual Coupon Payments/Current Market Price of a Bond
    Yield to Maturity= [Cash-Flows + (F+P/Number of years to Maturity) / (F+P/2)
    where F: Face Value of a bond
    P= Market Price of a bond
    When the credit issuers are solvent and there's no or every small change of default, then there bonds' yields are lower while their prices are higher. This is because they will most likely pay their debt obligations.
    That's the reasons economically-weak countries like Greece, Spain, Portugal and Argentina offer very high yields on their bonds.

    • @izzy3131
      @izzy3131 ปีที่แล้ว

      In other words - staking shitcoins

  • @nobody_X24
    @nobody_X24 3 ปีที่แล้ว

    Beautiful!!🙌🏾

  • @madhavishukla9816
    @madhavishukla9816 3 ปีที่แล้ว

    Finally my concepts are clear ✌️

  • @raecole4170
    @raecole4170 4 ปีที่แล้ว

    Simple , and accurate

  • @keatongroom
    @keatongroom 5 ปีที่แล้ว

    Beautiful explanation

  • @theoriserra1397
    @theoriserra1397 2 ปีที่แล้ว

    Very good and easy explanation. Cheers.

  • @Captainziadkhan
    @Captainziadkhan 6 ปีที่แล้ว

    love u khan... u r always awesome

  • @JudaiGaeMaino
    @JudaiGaeMaino 9 ปีที่แล้ว +4

    Thank you so much:) I love that you have the subtitle in the video

  • @honggwan.
    @honggwan. 3 ปีที่แล้ว

    Thank you for the video. It was easy to understand and informative. Thanks. 감사합니다!

  • @samsammbugua6234
    @samsammbugua6234 หลายเดือนก่อน

    A great explanation on the effect of interest rates on bond prices. I really needed this👏👏

  • @reallll2778
    @reallll2778 2 หลายเดือนก่อน

    Great video I finally get it thank you so much!

  • @shamimurr
    @shamimurr 2 ปีที่แล้ว

    I am proudly saying Bangladeshi , Khan come from the same country.

  • @ftw08
    @ftw08 2 ปีที่แล้ว

    Awesome video! Thank you!!!

  • @hafizahharris
    @hafizahharris 5 ปีที่แล้ว

    Thank you sir!

  • @pashuku
    @pashuku 4 ปีที่แล้ว

    Perfect. Thanks

  • @adonisdon819
    @adonisdon819 3 ปีที่แล้ว

    Thank you very much, very helpful ❤️

  • @gerardobombin228
    @gerardobombin228 2 ปีที่แล้ว

    Finally, I get it! Thanks!

  • @user-wh1nr9rr1h
    @user-wh1nr9rr1h 3 ปีที่แล้ว

    Great explanation !

  • @jz5748
    @jz5748 4 ปีที่แล้ว

    i need this now

  • @cna9708
    @cna9708 3 ปีที่แล้ว

    Sick calculator. Nicely explained aswell.

  • @jinpingxi9748
    @jinpingxi9748 3 ปีที่แล้ว

    people at Khan academy are such good teachers

  • @tonywallens217
    @tonywallens217 3 ปีที่แล้ว +8

    Never thought Id watch another Khan Academy video again in my life.

    • @abuturki4460
      @abuturki4460 3 ปีที่แล้ว

      You don't know what you are missing

  • @HezekiahDomowski
    @HezekiahDomowski 7 ปีที่แล้ว

    I like the way you think, this makes a lot of sense to me

  • @giniwelle
    @giniwelle ปีที่แล้ว

    Amazingly well done.

  • @khushaliraval9434
    @khushaliraval9434 2 ปีที่แล้ว

    Yes, it was amazing thanks!

  • @himanshiwadhwa9868
    @himanshiwadhwa9868 2 ปีที่แล้ว

    Very well explained!

  • @armon8399
    @armon8399 2 ปีที่แล้ว

    Great explanation. Thanks

  • @nareshkoyalkar8370
    @nareshkoyalkar8370 3 ปีที่แล้ว

    thank you so much sir,good explanation that i ever seen before