That was excellent. Many just give the formula. Others show briefly how to get from the compound interest formula to the continuous compound interest formula; but this is the only video I've found that includes all the steps. It's so much more useful. When parts are missed out, because it's asumed that everybody understands, then some, like me, miss out. I need to know why, not just what. Thank you! I'm only doing this for fun. I don't need to know this. But my way of thinking is that it's not worth knowing something unless you know where it comes from. It leaves you with a lack of satisfaction. With this, you say "ah, now I get it".
so the derivation only works if r=1 or 100% rate? I am still trying to understand why r has to equal 1 in the derivation when any other r or rate would have a limit of 1 as n approaches infinity
On the second line of the equation I understand how you rearranged the equation, to get (1 +1/n/r)^n/r But how did you know to make the other exponent rt? I figured it would be t, but not rt. I know you're right I just want to understand the logic on how you knew. Thank you.
The reason why he raised it to the power of n/r, forcing him to multiply the exponent by rt, instead of letting n be the exponent that becomes part of e is because that wouldn't result in the value of e as n approaches infinity. Logically, if both instances of n in the limit for e are replaced by n/r, then as you input increasingly large n values (approaching infinity), they will always be equal to each other, so it's the same as inputting a single "x", even if "n/r" reaches infinity sooner or later than x. However, if the exponent is n and the inside is n/r, they will be increasing at different rates and won't equal the same limit.
THANK YOU for explaining the steps in detail. Great teacher!
Thank you so much! I'm using this for learning about the continuous interest formula for my Precalculus II class.
damn, this is algebra 2 now, and taught a bit in algebra 1
Thak you my freaking god I was searching for that transformation step right there for so long
You are very welcome! I appreciate your comment. 😀
That was excellent. Many just give the formula. Others show briefly how to get from the compound interest formula to the continuous compound interest formula; but this is the only video I've found that includes all the steps. It's so much more useful. When parts are missed out, because it's asumed that everybody understands, then some, like me, miss out. I need to know why, not just what. Thank you! I'm only doing this for fun. I don't need to know this. But my way of thinking is that it's not worth knowing something unless you know where it comes from. It leaves you with a lack of satisfaction. With this, you say "ah, now I get it".
Thank you! I greatly appreciate your comment.
Awesome video! Nice, simple and easy to understand!
Thank you so much! this is very helpful as i'm reviewing this subject
so the derivation only works if r=1 or 100% rate? I am still trying to understand why r has to equal 1 in the derivation when any other r or rate would have a limit of 1 as n approaches infinity
Fantastic explanation!!🎉
On the second line of the equation I understand how you rearranged the equation, to get (1 +1/n/r)^n/r But how did you know to make the other exponent rt? I figured it would be t, but not rt. I know you're right I just want to understand the logic on how you knew. Thank you.
The reason why he raised it to the power of n/r, forcing him to multiply the exponent by rt, instead of letting n be the exponent that becomes part of e is because that wouldn't result in the value of e as n approaches infinity. Logically, if both instances of n in the limit for e are replaced by n/r, then as you input increasingly large n values (approaching infinity), they will always be equal to each other, so it's the same as inputting a single "x", even if "n/r" reaches infinity sooner or later than x. However, if the exponent is n and the inside is n/r, they will be increasing at different rates and won't equal the same limit.
@@arjunchopra5203 he asked 7 years before bro
Awesome explanation! Thanks a lot Mathispower4u. I'm definitely following your blog :)
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How are you? May the Lord bless and keep you in Jesus name amen.
With much love,
Aunty Bee
Thanks for this video! Helped so much.
Great explanation, very clear.
Great explanation. Thanks.
thanks a lot for the clearly explained lesson
Nice one, thanks a lot!
Thanks a lot, great explanation.
verrrrrrrrrrrrrrrrrrrrry helpful indeed.
Good one
Thanks for this!
THANK YOU !!!!
Thank you sooooooooo much!
That makes sense
Thanks buddy!