Many teachers and professors in school were never that smart and even most of the best ones don't want to provide you the best, fastest, and most efficient way to do things. If you ever have an excellent teacher, they will always make learning extremely easy and make you think that the subject is not hard to learn. The worst educators make everything almost impossible to learn and you eventually believe almost every subject is out of your reach.
Thank you for explaining this to me in a logical perspective. I couldn’t remember the equation for this particular method, so I had to do everything by hand every time I dealt with compounding interest.
I liked this video after 12 seconds of watching. This is exactly the case when math is a useful and practical skill. It is called a complex % and this is a very simple and elegant solution.
In school they just tell taou the formula and how to use it. They tell you the waht and the application. This is very useful in understanding how it works
Ok, let me tell ya how compound interest works. If you have a $10k balance on a credit card with a 25% APR interest rate, if you let the interest accumulate over a year, you will not owe 25% more, but 28% (=exp(0.25)-1) more, because the interest is compounded instantaneously. Thanks Euler :-/
Use formula: p’ = p(1 - P/100)^Y Let p’ = new price, p = original price, P = percentage of decrease, Y = years Here’s the useless formula for p’ when Y=5: p’ = (-P^5 + 500P^4 - 10^5P^3 + 10^7P^2 - 5*10^8P + 10^10)p / 10^10
Sir i think it is 7244 something because puchased vehicle it is 24500 So it will be decreased 7 percentage per year so the First year is 24500 of 7 % =1715 Second year 22785 %14=19595 Third year19595 of 21%=15480 Fourth year 15480 of 28=11145 Fith year 11145 of 35 percentage=7244 I think
Karthik what are you saying? Its 100% wrong. 7% decrease every year, but how you write its that the 1. year decrease 7%, and then improves decrease 14% only per 1 year?? And then 21% decrease only per the other next year? .....etc.....? Its absolutely WRONG. You you want believe us, in 5 years will decrease for a TOTAL 7%+14%+21%+28%+35%= *"105%"* !! NO PLEASE
Sure. Let V be the value of the car, and t be the time in years. Depreciation rate governs the following equation, where r is an unknown rate constant. dV/dt = -r*V Initial condition at t=0. V = 24500. This is the simplest kind of diffEQ you'll solve on the first day in the class. Simply treat the Leibnitz notation as a fraction, and separate the variables as such: dV/V = -r*dt Integrate both sides: ln(V) = -r*t + c Exponentiate both sides: V = e^(-r*t + c) Let C = e^c. Thus: V = C*e^(-r*t) The initial condition directly tells us C = 24500. When t=1, we want V to equal 24500*0.93. Thus: e^(-r) = 0.93 r = -ln(0.93) = 0.07257 Thus: V(t) = 24500*e^(-0.07257*t) Plug in t = 5 years, and get: V(5 years) = $17044
Can we all agree that 1% of $24,500= $245 with that in mind $245 x 7 = $1,715 or 7% per year now take that 1,715 x 5 years= 8,575. Total 24,500 - 8,575 = 15,925 or a 35% devaluation This .93 multiplication is throwing me off. If the car is worth $17,044.37 five years later that means the car only lost roughly 30.43% not 35%
I can see your confusion. However in this example, he is using compounding depreciation, meaning that the 7% depreciation is being applied to the new value after each years decline in value. Eg. First year it loses $1715 changing the cars value to $22785. When it depreciates by 7% again, that is spplied to the new price of $22785 resulting in a depreciation of approx $1595. Slightly less than the original depreciation. This is similar to how interest on a savings account works. After each interest payment is credited to your account, the next installment of interest will be determined by that new value, not the starting amount. If he stated that the vehicle would lose 7% of its 'original value' across 5 years then you could simply subtract 35% of its starting value as that is just a straight Percentage Change.
But isn't this under the assumption that the value is decreasing based on the value at the end of each year? I had actually assumed it depreciates on a flat rate of 7%*24'500.
It would be great before you begin calculating to reveal the equation.... that way, the material can better be understood....Therefore, what is the proof equation required to check your result?
For a problem like this, it requires tedious arithmetic to solve it completely by hand, so it isn't something you are expected to do in practice. In the days before calculators existed, people would solve it with slide rules. There are already plenty of calculators for depreciation and interest for free online, so it isn't a problem you really have to solve in practice. In general, exponential decay has plenty of real world applications. Some other examples: Heat transfer Control systems RC and RL electrical circuits, one such application is electronic timer circuits Vibration damping Acoustics of decaying sounds
Because 1/(1 + p) is not the same thing as (1 - p). It is for small values of p, but the larger the value of p, the greater the difference between these two.
I am quite conflicted by this word problem. I saw this as a geometric sequence word problem therefore; a5 = 24,500 × 0.93^5-1 a5 = 18,327.27 But how come the answer is 17,044.36? Was it not a geometric sequence word problem per se?
Your answer is wrong because you are calculating the decrease (which is constant a percentage at 7%) But the thing is the machine is depreciating by 7% of the remaining value every year (or like a compounded annual decrease). By approaching this problem as geometric sequence you keeping depreciating the value as a constant I.e. 7% of 24500 whereas it should be 7% of the remaining value of the machine. For example depreciation for one year will be 1715. So the depreciation for the second year will be calculated on the remaining value I.e 7% of 22785 I.e. 1594.94 and so on for the next year upto 5 years. This way of depreciating is also known as written down value method. Hope it helps😊
@@aarusharya3416 Man your answer is right but it's a lengthy process and we are finding an easier and shorter way and Geometrical sequence is the way to go. As you can see the depreciation rate is constant, hence there exists a common ratio "r" which is .93 and if we follow G.S formula which is ar^ n-1,we can easily find value after 5 years by putting a=24500,r= .93 and n=6. Hopefully you got it.
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This projector board setup is great, very handy for all.
Hahah if only they explained things this well in school id be fine 😅
Many teachers and professors in school were never that smart and even most of the best ones don't want to provide you the best, fastest, and most efficient way to do things. If you ever have an excellent teacher, they will always make learning extremely easy and make you think that the subject is not hard to learn. The worst educators make everything almost impossible to learn and you eventually believe almost every subject is out of your reach.
😂yes
Mine taught it like this
They do ! Principal Value * percent to the nth power, where n is the number of years. You just gotta pay attention !
Didn't work for me, she was too gorgeous, I stop day dreaming. She kept giving me "F". Oh zuck, I didn't know what she meant back then.
Percentages where one of the toughest for me
Thank you for this lesson
Something we can use
This guy is a delight.
This guy is fantastic!
This man is phenomenal.
Thank you for explaining this to me in a logical perspective. I couldn’t remember the equation for this particular method, so I had to do everything by hand every time I dealt with compounding interest.
You're very welcome!
I just love this channel
Nice. I just found out my cars current value and its trade in value after paying it off.
lol im about to do that right now .. since we got 2 more years left on it .. with low miles on it ..
Just plain inspirational, nice job with all your videos.
I liked this video after 12 seconds of watching. This is exactly the case when math is a useful and practical skill.
It is called a complex % and this is a very simple and elegant solution.
This is widely used in calculation of depreciation.
Amazing : Same goes for Compounding of money in positive.
You need to teach my calculus professor your methods of instruction. I learn as much in 60 seconds on TH-cam as I do an 2 hr class.
Maybe, you are more motivated while watching these videos, aren't you?
How simple! Thank You.
I had a similar problem. Thanks for reminding me to use this method.
In school they just tell taou the formula and how to use it. They tell you the waht and the application. This is very useful in understanding how it works
I'm so bad at math but thanks to you now i start to follow up.
nicely and simply explained!
these are great refreshers
I like you as a teacher I should have watch you more for my precal class right now I have to redo precal you can be a great help 👍
Always happy to hear that a precalc student is watching my videos.
Sir u are too good I was watching yt shorts while doing compound interest depreciation questions and this popped up
Those are some of my favorite problems. Exponential decay with percent decrease.
I have come into conclusion learning from TH-cam does well than in school
I always loved exponents :D
for our younger viewers...R&H is
AM only and without air conditioning...
Thanks for these videos 😊😊❤
You can even do that for 7% and subtract it from $24,500 coz 7⁵ is comparatively easier than calculating 25⁵... thankyou
Concept of compound interest.
Not to mention car payments and interest
Great videos
I was taught a similar topic in mathematics at high school. Interestingly the teacher were a Chinese too😁
He's American.
You make maths child’s play.
Gosh math is so cool
Appreciate from India ❤🎉
Finances maths be like, finance future value:
Students!! It was not your fault that you had given up your math classes. It was because you couldn’t have some right math teachers.
Thank you,sir
Ok, let me tell ya how compound interest works. If you have a $10k balance on a credit card with a 25% APR interest rate, if you let the interest accumulate over a year, you will not owe 25% more, but 28% (=exp(0.25)-1) more, because the interest is compounded instantaneously.
Thanks Euler :-/
A problem like this is best solved using a financial calculator like the HP 12C
Excellent video
Brilliant 👏 👏 👏
Depends if it is simple interest ir compound interest
This is called depreciation, but depreciation isn’t always calculated by a linear factor.
Ok, so this is just a math example, I suppose.
Love this!
I have a couple of math questions on quadratic equations I would like to ask you about...would it be okay to ask? I really would like help.
Cars don't decrease in value any more.
Ha, that's true!
Use formula:
p’ = p(1 - P/100)^Y
Let p’ = new price, p = original price, P = percentage of decrease, Y = years
Here’s the useless formula for p’ when Y=5:
p’ = (-P^5 + 500P^4 - 10^5P^3 + 10^7P^2 - 5*10^8P + 10^10)p / 10^10
Which is what he did?
@@yodaami yes
that's exactly what he did.
@@qwhfjd correct
It's a formula, guys. Some people like to remember formulas.
Thank you!
Fascinating...I did the following 7% * per year for 5 = 35% of 24,500 =8575
Nice I like your content
Thanks~
Elegant ❤
I’m smart but average in math- this gentleman is awesome
Ahhh i see that. Thank you.
Not me expecting him to put it on a graph 💀
A(t)=p(1+r/n)^nt
P equals initial amount
R equals rate
N equals amount of times broken each year
T equals.years
Yup, for the question in the video, n=1.
Thank you for the formula
That’s great but let’s make it more realistic and change that 7% to 10% per year for depreciation.😅
And what if my sadistic math teacher prohibits the use of a calculator?
you are a great
Thank you.
Just do I=PRT/100
P=Principal, R= Rate of intrest increased by 1 year, T= Time, I=Intrest
I don’t want to ask for much, but can we get full 10 minute videos again?
I am currently focusing on making the short videos for now.
I will definitely get back to making full videos soon.
that's why we study numerical sequences
This, but without the calculator would be fun xD
hard to believe we put someone on the moon if people need a video explanation for that
Should you not use: 24.500 . (1/1.07)^5? Or 24.500 / 1.07^5?
That's a very optimal way to do it. 😅
thank you
Only that depreciation in accounting is linear, so the value would be $24,500-(5*(-7%)*$24,500) = $15,925 😊
My life has became way too much easier now
that was a question from my first grade 9 test
professor, you can use series and sequence
n=5 summation n= 1 (24, 500) (.07) ^ (5n-5)/3
Sir i think it is 7244 something because puchased vehicle it is 24500
So it will be decreased 7 percentage per year so the
First year is 24500 of 7 % =1715
Second year 22785 %14=19595
Third year19595 of 21%=15480
Fourth year 15480 of 28=11145
Fith year 11145 of 35 percentage=7244
I think
Karthik what are you saying? Its 100% wrong. 7% decrease every year, but how you write its that the 1. year decrease 7%, and then improves decrease 14% only per 1 year?? And then 21% decrease only per the other next year? .....etc.....? Its absolutely WRONG. You you want believe us, in 5 years will decrease for a TOTAL 7%+14%+21%+28%+35%= *"105%"* !! NO PLEASE
Can we use differential equations to solve this question?
Sure. Let V be the value of the car, and t be the time in years.
Depreciation rate governs the following equation, where r is an unknown rate constant.
dV/dt = -r*V
Initial condition at t=0. V = 24500.
This is the simplest kind of diffEQ you'll solve on the first day in the class. Simply treat the Leibnitz notation as a fraction, and separate the variables as such:
dV/V = -r*dt
Integrate both sides:
ln(V) = -r*t + c
Exponentiate both sides:
V = e^(-r*t + c)
Let C = e^c. Thus:
V = C*e^(-r*t)
The initial condition directly tells us C = 24500. When t=1, we want V to equal 24500*0.93. Thus:
e^(-r) = 0.93
r = -ln(0.93) = 0.07257
Thus:
V(t) = 24500*e^(-0.07257*t)
Plug in t = 5 years, and get:
V(5 years) = $17044
Clever.
Can we all agree that 1% of $24,500= $245 with that in mind $245 x 7 = $1,715 or 7% per year now take that 1,715 x 5 years= 8,575.
Total 24,500 - 8,575 = 15,925 or a 35% devaluation
This .93 multiplication is throwing me off. If the car is worth $17,044.37 five years later that means the car only lost roughly 30.43% not 35%
I can see your confusion. However in this example, he is using compounding depreciation, meaning that the 7% depreciation is being applied to the new value after each years decline in value.
Eg. First year it loses $1715 changing the cars value to $22785. When it depreciates by 7% again, that is spplied to the new price of $22785 resulting in a depreciation of approx $1595. Slightly less than the original depreciation.
This is similar to how interest on a savings account works. After each interest payment is credited to your account, the next installment of interest will be determined by that new value, not the starting amount.
If he stated that the vehicle would lose 7% of its 'original value' across 5 years then you could simply subtract 35% of its starting value as that is just a straight Percentage Change.
@@alexc1512 Makes perfect sense if 7% is based on the annual value and not the initial cost.
Thank you for taking the time Alex
That’s why it says per year
Forgot about 4% inflation
But isn't this under the assumption that the value is decreasing based on the value at the end of each year? I had actually assumed it depreciates on a flat rate of 7%*24'500.
Why take 5 power and why not multiply by 5?
It would be great before you begin calculating to reveal the equation.... that way, the material can better be understood....Therefore, what is the proof equation required to check your result?
I'm wondering if it's 17 k Parked for 5 years,or 5 years with average milage? It makes a difference.
Just focus only on the car value not all the other details
The problem is we can't use the calculator during exam.. need an easier way
For problems such as this, exact answers are going to take a long time without a calculator.
How if you reverse the question on devalued car
Swell. Now I can calculate the progress of Bidenomics preying upon the value of my money.
056
25
---
306
Ok?
I could use this math.
We dont use calculators in school and colleges in India. Is this a school math problem or a general daily life math?
For a problem like this, it requires tedious arithmetic to solve it completely by hand, so it isn't something you are expected to do in practice. In the days before calculators existed, people would solve it with slide rules.
There are already plenty of calculators for depreciation and interest for free online, so it isn't a problem you really have to solve in practice.
In general, exponential decay has plenty of real world applications. Some other examples:
Heat transfer
Control systems
RC and RL electrical circuits, one such application is electronic timer circuits
Vibration damping
Acoustics of decaying sounds
Use compound interest formula
This must be a high quality car with low mileage....after 5 yrs..... 😂❤
Or take 7% and subtract wtv that is from the total ad keep doing that 5 times
Price = 24500
Depreciation = 7%
I = 1
Do while I
But the base value decreased after the first year. So now it's 7% of 22785...
Hi! I like this example, but...
If you buy a new car today, you can sell it tomorrow for an amount less than 25% of the price you paid.
Why can't it just be a flat 35% (7*5) of total decrease over the course of 5 years?
24500/100*35
245 * 35 = 8575
24500 - 8575 = 15925
Makes no sense, is it 7% of the original price ? Shouldn't it adjust to the value of the car for that year?
What type of car is this? BMWs are @ 40% after 5 years
It's just a hypothetical car.
But isn't difficult to multiply all this at the end to get the answer
For that reason, you want to use the exponential method, written in red in the video.
Why is 24500/1,07^5 not correct?
Because 1/(1 + p) is not the same thing as (1 - p). It is for small values of p, but the larger the value of p, the greater the difference between these two.
Is there trick to the .93⁵ faster that would be helpful
So?! Compound is the opposite, where 24000×[1.07]⁵...
Why is it 24900(.93)^5 not {24900(.93)}*5? Pls someone explain the difference 😢
I am quite conflicted by this word problem. I saw this as a geometric sequence word problem therefore;
a5 = 24,500 × 0.93^5-1
a5 = 18,327.27
But how come the answer is 17,044.36? Was it not a geometric sequence word problem per se?
Man,you actually had to find a6 because initial value is taken as a1 and the value after 5 years must be equal to a6.
Got it?
@@servantofIslamA ooohhh, thank you man. I did not think of that
@@user-bu9xh4sg6v Happy to help, brother
Your answer is wrong because you are calculating the decrease (which is constant a percentage at 7%)
But the thing is the machine is depreciating by 7% of the remaining value every year (or like a compounded annual decrease). By approaching this problem as geometric sequence you keeping depreciating the value as a constant I.e. 7% of 24500 whereas it should be 7% of the remaining value of the machine. For example depreciation for one year will be 1715. So the depreciation for the second year will be calculated on the remaining value I.e 7% of 22785 I.e. 1594.94 and so on for the next year upto 5 years. This way of depreciating is also known as written down value method. Hope it helps😊
@@aarusharya3416 Man your answer is right but it's a lengthy process and we are finding an easier and shorter way and Geometrical sequence is the way to go.
As you can see the depreciation rate is constant, hence there exists a common ratio "r" which is .93 and if we follow G.S formula which is ar^ n-1,we can easily find value after 5 years by putting a=24500,r= .93 and n=6.
Hopefully you got it.
If it’s 7% for a year and they want five years why not just make it 35% or 24,500(.65)=?
Actually... depreciation of assets is not calculated with compound rates. You should have given the example of bank interests.
Actually a depreciates 20% as soon as you drive it off the lot.
Depends on the car.