Physics Ninja looks at the derivation of the Amortization Formula used to calculate the monthly payment on a loan or mortgage
Пікірлер: 61
@watch77494 ай бұрын
You sir, are awesome! This is the BEST explanation I have come across! I don't know if its because loan sellers don't want to be super clear or if they just lack the math background, but I hadn't found any of their explanations to make sense. This made it crystal clear, and I feel so much safer knowing what I'm getting myself into!
@user-rz5xm2be9k6 ай бұрын
Thank you very much. Was looking for how the loan was calculated and only getting the formula everywhere. But your explanation clears it out. Thank you!
@boredomgotmehere11 ай бұрын
What a wonderful and thoughtful explanation. You not only gave the superficial meaning but the contextual meaning by doing the heavy lifting of proving the geometry series. Super thankful.
@PhysicsNinja11 ай бұрын
Thanks for the comment. I appreciate it.
@avankm7742 жыл бұрын
I cannot give the amount of likes that I want. This video made my night after a whole day looking for explanations on how to calculate this and also how to make the table for each month. Awesome video and keep up the good work, thank you!
@PhysicsNinja2 жыл бұрын
Thanks for the support!
@EverApprentice11 ай бұрын
I've been looking for how this formula is determined all over the internet, and finally here it is!! Thanks for the amazing explanation.
@tomera798 ай бұрын
Thank you. Very clear and useful! I wish more tutorials on the Internet were like this one!
@fozzydare79876 ай бұрын
I’m determined to understand this fully - it’s going to take more than one watch 😅 Thank you for your work
@PhysicsNinja6 ай бұрын
It probably took me 4-5 times
@otis2992 жыл бұрын
Love your videos! Just FYI, the dollar sign goes in front of a dollar amount e.g., $100.45 or $1M for one million dollars. The lesser used cent sign “¢” would go after the number and would be omitted in the presence of a dollar sign e.g., 99¢. Thanks for all you do!
@williamrhopkins14 күн бұрын
Very nice -- a couple of nuances. The compounding period can vary. In your example interest is compounded monthly. In Canada mortgagee rates are compounded semi annually so the monthly interest rate is (1+r/2)^(2/12). Often banks actually calculate a daily interest rate. For semi annual compounding the daily rate for non leap years is (1+r/2)^(2/365) and for leap years (1+r/2)^(2/366). This allows for calculating weekly and biweekly repayments. For monthly payments the amount of interest that is applied to the principle will vary depending on the length of the month. Lastly the financial literacy of sales people and loan managers is abysmal -- just ask any of them to explain how the loan is amortized or challenge them to produce a spreadsheet that provides an amortization schedule. Come on this is high school math -- no calculus involved.
@wanghonghui15532 жыл бұрын
Sir, you are a treasure for our society!
@arielfuxman8868 Жыл бұрын
This makes so much sense. Excellent for us Mathematically oriented people.
@PhysicsNinja Жыл бұрын
Thanks for watching.
@EverApprentice Жыл бұрын
Great video. Clear explanation and Python demonstration on this prolonged question I have in mind. Thanks for that!
@makk348010 ай бұрын
just one line for the video: AMAZING EXPLANATION!
@PhysicsNinja10 ай бұрын
Thank you
@fozzydare79876 ай бұрын
I’m determined to understand this fully - it’s going to take more than one watch 😅 Thank you for your workI
@ramineslami60534 ай бұрын
thank you so much. it was really clear and useful.
@patomatma8 ай бұрын
awesome job
@orionfollett70562 жыл бұрын
Isn't dividing the annual interest rate by 12 to get the monthly rate an approximation? Going up 12% a year is not the same as going up 1% a month. Anyone can easily see this by just inputting it into a calculator if they don't believe me. (1+.12)^1 = 1.12 =/= (1+.01)^12 = 1.1268... I know this is how most calculators work still but I wonder why this approximation is always used?
@ScienceDiscoverer Жыл бұрын
I noticed this too... I guess its just because of the en.wikipedia.org/wiki/Time_value_of_money If you pay your loan in the end of the year in one payment, you will have to pay more, as all the payment will be in the future, thus it cost will be more than if you paid small sum every day or every month. You are still paying bulk of the loan in the future, but few payments in first month worth much more than those in the end, so the end interest sum is lower in this case, although the "annual" interest stays the same!
@ecolibertarian56227 ай бұрын
The assumption r=R/12 is never used in the actual derivation so the formula still stands. And you are right, r would be the monthly interest rate that translates to the R annual rate. i.e (1+r)^12 = R.
@JAMYLIVES2 жыл бұрын
Wow! wonderfully explained. Thank you!
@PhysicsNinja2 жыл бұрын
Glad it was helpful!
@bansheedearg Жыл бұрын
Thanks for sharing the python code, for python3, print() is a function so you'll have to wrap the strings in parens. Great video, thank you!
@majid18858 ай бұрын
great video, thank you
@09blueumbrella3 жыл бұрын
This was very helpful. Thank you!
@arkleston32997 ай бұрын
Thank you for explaining this so well!
@PhysicsNinja7 ай бұрын
You're very welcome!
@woojin8369 Жыл бұрын
Thank you for exploring your curioisty and your due dilligence! This was inisghtful :))
@blackblather9 ай бұрын
wonderful explanation. Thank you
@CliffSedge-nu5fv4 ай бұрын
I've actually been looking for a derivation of present value given future value, but I think I can use this as a guide for how to set it up.
@prashantdahiya711 Жыл бұрын
Thank You for the same, brilliant explanation.
@juant4821 Жыл бұрын
Excellent derivation!
@cradleofrelaxation6473 Жыл бұрын
Thanks. I was like how the heck did my back come up with the money payment?
@Kappy0001 Жыл бұрын
Very nice work! Thanks!
@b.c.28366 ай бұрын
Taking python class, already built a calculator for amortization total interest paid, but no wanted to bulid one that took into account extra principal payments and I was looking for that formula.
@youpattube13 жыл бұрын
Thanks for the derivation. But...... And this may sound like something a flat earther would ask, but it seems like interest gets figured in twice. To get the Current Payment, you take the Prevous Balance, subtract the previous payment, and add the interest paid on the previous balance. But the interest was already figured in the monthly payment. I'm just a little confused.
@martincstee5335 Жыл бұрын
This video explains it better: kzfaq.info/get/bejne/qNp5daqZx7nJco0.html&ab_channel=DrBobMaths%28OnlineMathsTuition%29 Essentially the first month when you obtain the loan, you do not make any payment. The interest for the first month accrues at the end of the first month, regardless if you make the payment either at the end of the first month or the beginning of the second month. So, at the end of the first month interest was only factored in for the first month. At the end of the second month, interest was only factored in for the balance minus the first constant payment. One can argue that the constant monthly payment M already contains the interest Pnr. But at least for the first month the interest of P0r is correct. Maybe some math genius can derive a more logical formula that can save us all some interest payment.
@susovandey45312 жыл бұрын
Awesome brother
@funnelboss57212 жыл бұрын
Awesome Thanks for sharing, may i ask why simplify geometry part (2) - (1)?
@Epistemer Жыл бұрын
Thanks man, great explanation :)
@adamidrisnuh4328 Жыл бұрын
Thank you... Very much appreciate. If my lecturer teach this formula, i think my financial management will get A.
@gtrecc545410 ай бұрын
Great video
@user-fy4iq6if4z Жыл бұрын
짱입니당
@matteogriseri6513 Жыл бұрын
THANK YOU FINALLY
@NeonCurveZz2 жыл бұрын
You got rid of the porsche? I thought you were planning on getting an R8 next?!
@NgocTruong-zt9dp2 ай бұрын
Bro can you explain why p1 = p0 -M +p0*r ?
@shivankagrawal97642 жыл бұрын
16:21 But why did you multiply X by (1+r)
@bansheedearg Жыл бұрын
So he could eliminate all the internal terms of (1+r)^n. If I have 1 + A + A*A + A*A*A + A^4 + A^5, I can multiply and divide by A - 1 to get (A^6 - 1) / (A - 1), or why he subtracted equation (2) from equation (1)
@Scott-jk5zk2 жыл бұрын
18:26 how does (1+r)X-X=rX ?
@Scott-jk5zk2 жыл бұрын
one sec X((1+r)-1) X(r+1-1) X(r) rX I see now
@user-sm1fh1iy4p11 ай бұрын
Well i can explain this a little more simply. Just explain what annuities are and how it's formula is derived. Done!
@PhysicsNinja11 ай бұрын
Clear as mud!
@truthfirst9488 Жыл бұрын
Is this for USA or Canada?
@TusharMajumdar2 жыл бұрын
Thank you very much. Was looking for how the loan was calculated and only getting the formula everywhere. But your explanation clears it out. Thank you!
@fozzydare79876 ай бұрын
I’m determined to understand this fully - it’s going to take more than one watch 😅 Thank you for your work