Derivation of Loan/Mortgage Monthly Payment Formula
Physics Ninja looks at the derivation of the Amortization Formula used to calculate the monthly payment on a loan or mortgage
Жүктеу.....
Пікірлер: 60
@user-rz5xm2be9k5 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!
@watch77493 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!
@boredomgotmehere10 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.
@PhysicsNinja
10 ай бұрын
Thanks for the comment. I appreciate it.
@EverApprentice10 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.
@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!
@PhysicsNinja
2 жыл бұрын
Thanks for the support!
@tomera797 ай бұрын
Thank you. Very clear and useful! I wish more tutorials on the Internet were like this one!
@fozzydare79875 ай бұрын
I’m determined to understand this fully - it’s going to take more than one watch 😅 Thank you for your work
@PhysicsNinja
5 ай бұрын
It probably took me 4-5 times
@EverApprentice Жыл бұрын
Great video. Clear explanation and Python demonstration on this prolonged question I have in mind. Thanks for that!
@wanghonghui15532 жыл бұрын
Sir, you are a treasure for our society!
@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!
@09blueumbrella2 жыл бұрын
This was very helpful. Thank you!
@arielfuxman886811 ай бұрын
This makes so much sense. Excellent for us Mathematically oriented people.
@PhysicsNinja
11 ай бұрын
Thanks for watching.
@prashantdahiya711 Жыл бұрын
Thank You for the same, brilliant explanation.
@woojin8369 Жыл бұрын
Thank you for exploring your curioisty and your due dilligence! This was inisghtful :))
@fozzydare79875 ай бұрын
I’m determined to understand this fully - it’s going to take more than one watch 😅 Thank you for your workI
@Kappy0001 Жыл бұрын
Very nice work! Thanks!
@makk34809 ай бұрын
just one line for the video: AMAZING EXPLANATION!
@PhysicsNinja
9 ай бұрын
Thank you
@JAMYLIVES2 жыл бұрын
Wow! wonderfully explained. Thank you!
@PhysicsNinja
2 жыл бұрын
Glad it was helpful!
@ramineslami60533 ай бұрын
thank you so much. it was really clear and useful.
@arkleston32996 ай бұрын
Thank you for explaining this so well!
@PhysicsNinja
6 ай бұрын
You're very welcome!
@blackblather8 ай бұрын
wonderful explanation. Thank you
@juant4821 Жыл бұрын
Excellent derivation!
@Epistemer Жыл бұрын
Thanks man, great explanation :)
@patomatma7 ай бұрын
awesome job
@majid18857 ай бұрын
great video, thank you
@susovandey45312 жыл бұрын
Awesome brother
@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!
@gtrecc54549 ай бұрын
Great video
@funnelboss57212 жыл бұрын
Awesome Thanks for sharing, may i ask why simplify geometry part (2) - (1)?
@matteogriseri6513 Жыл бұрын
THANK YOU FINALLY
@user-fy4iq6if4z Жыл бұрын
짱입니당
@b.c.28365 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.
@adamidrisnuh4328 Жыл бұрын
Thank you... Very much appreciate. If my lecturer teach this formula, i think my financial management will get A.
@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!
@ecolibertarian5622
6 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.
@CliffSedge-nu5fv3 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.
@cradleofrelaxation647311 ай бұрын
Thanks. I was like how the heck did my back come up with the money payment?
@NeonCurveZz2 жыл бұрын
You got rid of the porsche? I thought you were planning on getting an R8 next?!
@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: kzread.info/dash/bejne/pKh9pKmhkrbLcrw.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.
@shivankagrawal9764 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-jk5zk
2 жыл бұрын
one sec X((1+r)-1) X(r+1-1) X(r) rX I see now
@NgocTruong-zt9dpАй бұрын
Bro can you explain why p1 = p0 -M +p0*r ?
@user-sm1fh1iy4p9 ай бұрын
Well i can explain this a little more simply. Just explain what annuities are and how it's formula is derived. Done!
@PhysicsNinja
9 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!
@fozzydare79875 ай бұрын
I’m determined to understand this fully - it’s going to take more than one watch 😅 Thank you for your work
Пікірлер: 60
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!
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!
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.
@PhysicsNinja
10 ай бұрын
Thanks for the comment. I appreciate it.
I've been looking for how this formula is determined all over the internet, and finally here it is!! Thanks for the amazing explanation.
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!
@PhysicsNinja
2 жыл бұрын
Thanks for the support!
Thank you. Very clear and useful! I wish more tutorials on the Internet were like this one!
I’m determined to understand this fully - it’s going to take more than one watch 😅 Thank you for your work
@PhysicsNinja
5 ай бұрын
It probably took me 4-5 times
Great video. Clear explanation and Python demonstration on this prolonged question I have in mind. Thanks for that!
Sir, you are a treasure for our society!
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!
This was very helpful. Thank you!
This makes so much sense. Excellent for us Mathematically oriented people.
@PhysicsNinja
11 ай бұрын
Thanks for watching.
Thank You for the same, brilliant explanation.
Thank you for exploring your curioisty and your due dilligence! This was inisghtful :))
I’m determined to understand this fully - it’s going to take more than one watch 😅 Thank you for your workI
Very nice work! Thanks!
just one line for the video: AMAZING EXPLANATION!
@PhysicsNinja
9 ай бұрын
Thank you
Wow! wonderfully explained. Thank you!
@PhysicsNinja
2 жыл бұрын
Glad it was helpful!
thank you so much. it was really clear and useful.
Thank you for explaining this so well!
@PhysicsNinja
6 ай бұрын
You're very welcome!
wonderful explanation. Thank you
Excellent derivation!
Thanks man, great explanation :)
awesome job
great video, thank you
Awesome brother
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!
Great video
Awesome Thanks for sharing, may i ask why simplify geometry part (2) - (1)?
THANK YOU FINALLY
짱입니당
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.
Thank you... Very much appreciate. If my lecturer teach this formula, i think my financial management will get A.
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!
@ecolibertarian5622
6 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.
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.
Thanks. I was like how the heck did my back come up with the money payment?
You got rid of the porsche? I thought you were planning on getting an R8 next?!
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: kzread.info/dash/bejne/pKh9pKmhkrbLcrw.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.
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)
18:26 how does (1+r)X-X=rX ?
@Scott-jk5zk
2 жыл бұрын
one sec X((1+r)-1) X(r+1-1) X(r) rX I see now
Bro can you explain why p1 = p0 -M +p0*r ?
Well i can explain this a little more simply. Just explain what annuities are and how it's formula is derived. Done!
@PhysicsNinja
9 ай бұрын
Clear as mud!
Is this for USA or Canada?
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!
I’m determined to understand this fully - it’s going to take more than one watch 😅 Thank you for your work