Talk:2768: Definition of e - Revision history

68.42.184.67 at 10:28, 30 July 2025

2025-07-30T10:28:02Z

Bb777 at 01:19, 25 March 2025

2025-03-25T01:19:32Z

Jkshapiro: I was bold

2024-04-10T02:28:28Z

I was bold

162.158.74.25 at 00:12, 29 December 2023

2023-12-29T00:12:25Z

162.158.159.103: /* r = n * (2^(1/n) - 1) */

2023-12-29T00:01:56Z

‎r = n * (2^(1/n) - 1)

162.158.159.103: /* r = n * (2^(1/n) - 1) */

2023-12-28T23:58:48Z

‎r = n * (2^(1/n) - 1)

EebstertheGreat: /* r = n * (2^(1/n) - 1) */

2023-05-14T03:32:02Z

‎r = n * (2^(1/n) - 1)

Peregrine: Questioning the need to critique the realism of this as a business practice

2023-05-06T01:41:38Z

Questioning the need to critique the realism of this as a business practice

172.70.147.47: /* r = n * (2^(1/n) - 1) */

2023-05-04T23:51:58Z

‎r = n * (2^(1/n) - 1)

Miamiclay at 15:09, 4 May 2023

2023-05-04T15:09:46Z

← Older revision		Revision as of 10:28, 30 July 2025
Line 52:		Line 52:

	only if she gives it back! --[[User:Bb777\|[insert signature here]]] ([[User talk:Bb777\|talk]]) 01:19, 25 March 2025 (UTC)		only if she gives it back! --[[User:Bb777\|[insert signature here]]] ([[User talk:Bb777\|talk]]) 01:19, 25 March 2025 (UTC)
		+
		+	My read of this comic: Trying to explain e without using calculus is rather like trying to explain pi without using circles. The "compound interest" explanation has never held water for me. [[Special:Contributions/68.42.184.67\|68.42.184.67]] 10:28, 30 July 2025 (UTC)

← Older revision		Revision as of 01:19, 25 March 2025
Line 50:		Line 50:

	Cut down the explanation of the title text. It was long, contradictory, and, I would argue, wrong. [[User:Jkshapiro\|Jkshapiro]] ([[User talk:Jkshapiro\|talk]]) 02:28, 10 April 2024 (UTC)		Cut down the explanation of the title text. It was long, contradictory, and, I would argue, wrong. [[User:Jkshapiro\|Jkshapiro]] ([[User talk:Jkshapiro\|talk]]) 02:28, 10 April 2024 (UTC)
		+
		+	only if she gives it back! --[[User:Bb777\|[insert signature here]]] ([[User talk:Bb777\|talk]]) 01:19, 25 March 2025 (UTC)

← Older revision		Revision as of 02:28, 10 April 2024
Line 48:		Line 48:
	The example in the comic would work better with a loan than with a deposit, because banks do typically use "annual interest rates" when quoting loans, but then he'd need to change the joke in the mouseover text.<br> {{unsigned ip\|162.158.159.103\|23:58, 28 December 2023}}		The example in the comic would work better with a loan than with a deposit, because banks do typically use "annual interest rates" when quoting loans, but then he'd need to change the joke in the mouseover text.<br> {{unsigned ip\|162.158.159.103\|23:58, 28 December 2023}}
	-- -- --<br>		-- -- --<br>
		+
		+	Cut down the explanation of the title text. It was long, contradictory, and, I would argue, wrong. [[User:Jkshapiro\|Jkshapiro]] ([[User talk:Jkshapiro\|talk]]) 02:28, 10 April 2024 (UTC)

@@ Line 46: / Line 46: @@
 All that said, most banks nowadays specifically quote only the APY for deposits (not surprising, since it's the bigger number and bigger looks better to the customer when you're talking interest crediting). So for that reason, you're correct that this XKCD is a bit misleading -- you don't ever see banks talking about the "interest rate" on deposits anymore; e.g. go to BankRate.com and you'll see a list of various banks' APY's -- labeled as such. But the comic is not wrong about the meaning of "annual interest rate".
-The example in the comic would work better with a loan than with a deposit, because banks do typically use "annual interest rates" when quoting loans, but then he'd need to change the joke in the mouseover text.<br>
+The example in the comic would work better with a loan than with a deposit, because banks do typically use "annual interest rates" when quoting loans, but then he'd need to change the joke in the mouseover text.<br> {{unsigned ip|162.158.159.103|23:58, 28 December 2023}}
 -- -- --<br>

← Older revision		Revision as of 00:01, 29 December 2023
Line 37:		Line 37:

	-- -- --<br>		-- -- --<br>
		+	[In response to the top comment in this section]
	No, that's not what "interest rate" typically means in the US. In the US, when a rate is quoted as an "annual interest rate", the rate quoted is merely a nominal amount, and when compounded at the specified compounding frequency over the course of a year will yield slightly more interest than the quoted nominal rate. What you have described would be called the "annual percentage yield" ("APY") in the US. To be clear: in the American usage of "interest rate", three elements are needed to properly specify the interest: 1) the nominal rate, 2) the length of time over which that rate would accrue at simple interest (i.e., the word "annual" in "100% annual interest" in the comic), and 3) the compounding period. However, it's traditional to quote annual rates, and I believe there are rules on compounding periods (I think it has to be daily, but not sure).		No, that's not what "interest rate" typically means in the US. In the US, when a rate is quoted as an "annual interest rate", the rate quoted is merely a nominal amount, and when compounded at the specified compounding frequency over the course of a year will yield slightly more interest than the quoted nominal rate. What you have described would be called the "annual percentage yield" ("APY") in the US. To be clear: in the American usage of "interest rate", three elements are needed to properly specify the interest: 1) the nominal rate, 2) the length of time over which that rate would accrue at simple interest (i.e., the word "annual" in "100% annual interest" in the comic), and 3) the compounding period. However, it's traditional to quote annual rates, and I believe there are rules on compounding periods (I think it has to be daily, but not sure).

← Older revision		Revision as of 23:58, 28 December 2023
Line 35:		Line 35:

	It's just the difference between measuring interest in APY and APR. A 100% rate compounded every minute has a 172% yield. The teacher must be talking about rate, because that's the only way to get $e at the end. [[User:EebstertheGreat\|EebstertheGreat]] ([[User talk:EebstertheGreat\|talk]]) 03:32, 14 May 2023 (UTC)		It's just the difference between measuring interest in APY and APR. A 100% rate compounded every minute has a 172% yield. The teacher must be talking about rate, because that's the only way to get $e at the end. [[User:EebstertheGreat\|EebstertheGreat]] ([[User talk:EebstertheGreat\|talk]]) 03:32, 14 May 2023 (UTC)
		+
		+	-- -- --<br>
		+	No, that's not what "interest rate" typically means in the US. In the US, when a rate is quoted as an "annual interest rate", the rate quoted is merely a nominal amount, and when compounded at the specified compounding frequency over the course of a year will yield slightly more interest than the quoted nominal rate. What you have described would be called the "annual percentage yield" ("APY") in the US. To be clear: in the American usage of "interest rate", three elements are needed to properly specify the interest: 1) the nominal rate, 2) the length of time over which that rate would accrue at simple interest (i.e., the word "annual" in "100% annual interest" in the comic), and 3) the compounding period. However, it's traditional to quote annual rates, and I believe there are rules on compounding periods (I think it has to be daily, but not sure).
		+
		+	If you don't believe me, check out this primer on the Truth in Savings regs, put out by the Federal Reserve: https://www.federalreserve.gov/boarddocs/caletters/2009/0914/09-14-attachment.pdf , e.g. the APY description on page 2. Or this CNN article: https://www.cnn.com/cnn-underscored/money/apy-vs-interest-rate
		+
		+	Now that's for deposits, as in the comic. For loans, we have the term "annual percentage rate", which, while sounding close to "annual percentage yield", is actually used in the same way as "interest rate" as I described above (that is, to find the actual interest charged over the compounding period you simply divide the nominal rate by the number of periods in a year). The difference between "interest rate" and "APR" is that fees have to be rolled into the APR calculation, to give a better sense of total cost of borrowing money. To be clear -- APR and APY are pretty different, mathematically speaking, suggesting that Americans interpret "rate" to be a nominal amount that won't compound to the quoted amount, while we interpret "yield" to be the effective amount that does compound to the quoted amount. And lest anyone feel otherwise, these usages are not "wrong" (or right, for that matter), they're merely convention.
		+
		+	All that said, most banks nowadays specifically quote only the APY for deposits (not surprising, since it's the bigger number and bigger looks better to the customer when you're talking interest crediting). So for that reason, you're correct that this XKCD is a bit misleading -- you don't ever see banks talking about the "interest rate" on deposits anymore; e.g. go to BankRate.com and you'll see a list of various banks' APY's -- labeled as such. But the comic is not wrong about the meaning of "annual interest rate".
		+
		+	The example in the comic would work better with a loan than with a deposit, because banks do typically use "annual interest rates" when quoting loans, but then he'd need to change the joke in the mouseover text.<br>
		+	-- -- --<br>

← Older revision		Revision as of 03:32, 14 May 2023
Line 32:		Line 32:

	As it stands, this explanation smacks of [[2623\|taking the fictional scenario way too literally]]. It spends a lot of words deconstructing the idea of "100% annual interest", instead of ''explaining the comic''. My interpretation is that we're meant to take the 100% at face value: [[1493\|it shouldn't work, but it does]]. -- [[User:Peregrine\|Peregrine]] ([[User talk:Peregrine\|talk]]) 01:41, 6 May 2023 (UTC)		As it stands, this explanation smacks of [[2623\|taking the fictional scenario way too literally]]. It spends a lot of words deconstructing the idea of "100% annual interest", instead of ''explaining the comic''. My interpretation is that we're meant to take the 100% at face value: [[1493\|it shouldn't work, but it does]]. -- [[User:Peregrine\|Peregrine]] ([[User talk:Peregrine\|talk]]) 01:41, 6 May 2023 (UTC)
		+
		+
		+	It's just the difference between measuring interest in APY and APR. A 100% rate compounded every minute has a 172% yield. The teacher must be talking about rate, because that's the only way to get $e at the end. [[User:EebstertheGreat\|EebstertheGreat]] ([[User talk:EebstertheGreat\|talk]]) 03:32, 14 May 2023 (UTC)

← Older revision		Revision as of 01:41, 6 May 2023
Line 30:		Line 30:
	::The difference between "compounded annually" and "compounded monthly" was/is that "compounded monthly" is computed on the "minimum monthly balance". Savings banks moved to "compounded daily" when computers meant that the work involved wasn't completely unreasonable. With "compounded daily", you get paid interest even if you have one day in the month when the balance was $0.01 and all the other days were $100K.		::The difference between "compounded annually" and "compounded monthly" was/is that "compounded monthly" is computed on the "minimum monthly balance". Savings banks moved to "compounded daily" when computers meant that the work involved wasn't completely unreasonable. With "compounded daily", you get paid interest even if you have one day in the month when the balance was $0.01 and all the other days were $100K.
	::If you are buying a 90 day bond, the interest really is quoted as n90/365 (or n90/360, or n*90/366 or %90/90, depending on the exchange rules). And if you re-invest, you get more. And you can do the same with over-night money (daily rollover). But that's "re-investment", not "daily-compounding". And the thing is, working out "true cost" is difficult for most people, and most people don't know and haven't thought about what "daily compounding" is, and probably wouldn't understand the math if they do think about it. It's easy to believe that teachers are miss-using the business terms used for ordinary savings accounts, but if so, that's unfortunate.		::If you are buying a 90 day bond, the interest really is quoted as n90/365 (or n90/360, or n*90/366 or %90/90, depending on the exchange rules). And if you re-invest, you get more. And you can do the same with over-night money (daily rollover). But that's "re-investment", not "daily-compounding". And the thing is, working out "true cost" is difficult for most people, and most people don't know and haven't thought about what "daily compounding" is, and probably wouldn't understand the math if they do think about it. It's easy to believe that teachers are miss-using the business terms used for ordinary savings accounts, but if so, that's unfortunate.
		+
		+	As it stands, this explanation smacks of [[2623\|taking the fictional scenario way too literally]]. It spends a lot of words deconstructing the idea of "100% annual interest", instead of ''explaining the comic''. My interpretation is that we're meant to take the 100% at face value: [[1493\|it shouldn't work, but it does]]. -- [[User:Peregrine\|Peregrine]] ([[User talk:Peregrine\|talk]]) 01:41, 6 May 2023 (UTC)

← Older revision		Revision as of 23:51, 4 May 2023
Line 28:		Line 28:
	::I read it as someone else, off-panel (traditionall Randall's voice, but not in this case?), who is describing a different time and who clearly didn't/doesn't grasp reality (did not get taught/listen that well, at school, seems convinced they did something clever), or can actually ignore the problems (like Beret Guy). But it could do with streamlining. ''Or'' various brief arguments for and against who is saying it, split up. [[Special:Contributions/172.70.162.161\|172.70.162.161]] 12:35, 4 May 2023 (UTC)		::I read it as someone else, off-panel (traditionall Randall's voice, but not in this case?), who is describing a different time and who clearly didn't/doesn't grasp reality (did not get taught/listen that well, at school, seems convinced they did something clever), or can actually ignore the problems (like Beret Guy). But it could do with streamlining. ''Or'' various brief arguments for and against who is saying it, split up. [[Special:Contributions/172.70.162.161\|172.70.162.161]] 12:35, 4 May 2023 (UTC)
	:::I initially (mis?)read “his bank” as reflecting not ownership, but where he banked, but you’re probably right. Either way, the whole thing seems both unclear as to the referents and somewhat misconceived - When a bank pays absurdly high rates, the last thing one would want is to acquire it! [[User:Miamiclay\|Miamiclay]] ([[User talk:Miamiclay\|talk]]) 15:09, 4 May 2023 (UTC)		:::I initially (mis?)read “his bank” as reflecting not ownership, but where he banked, but you’re probably right. Either way, the whole thing seems both unclear as to the referents and somewhat misconceived - When a bank pays absurdly high rates, the last thing one would want is to acquire it! [[User:Miamiclay\|Miamiclay]] ([[User talk:Miamiclay\|talk]]) 15:09, 4 May 2023 (UTC)
		+	::The difference between "compounded annually" and "compounded monthly" was/is that "compounded monthly" is computed on the "minimum monthly balance". Savings banks moved to "compounded daily" when computers meant that the work involved wasn't completely unreasonable. With "compounded daily", you get paid interest even if you have one day in the month when the balance was $0.01 and all the other days were $100K.
		+	::If you are buying a 90 day bond, the interest really is quoted as n90/365 (or n90/360, or n*90/366 or %90/90, depending on the exchange rules). And if you re-invest, you get more. And you can do the same with over-night money (daily rollover). But that's "re-investment", not "daily-compounding". And the thing is, working out "true cost" is difficult for most people, and most people don't know and haven't thought about what "daily compounding" is, and probably wouldn't understand the math if they do think about it. It's easy to believe that teachers are miss-using the business terms used for ordinary savings accounts, but if so, that's unfortunate.

← Older revision		Revision as of 15:09, 4 May 2023
Line 27:		Line 27:
	::Unremoved the last para. The teacher deecribed is male, '''Miss''' L is not.{{Citation needed}} But if the suggestion is that the narrating person is Miss L (after the year has passed?), then we have other problems to explain (how she thinks she got it to work, hypercompetent as she is but as impossible the setup is).		::Unremoved the last para. The teacher deecribed is male, '''Miss''' L is not.{{Citation needed}} But if the suggestion is that the narrating person is Miss L (after the year has passed?), then we have other problems to explain (how she thinks she got it to work, hypercompetent as she is but as impossible the setup is).
	::I read it as someone else, off-panel (traditionall Randall's voice, but not in this case?), who is describing a different time and who clearly didn't/doesn't grasp reality (did not get taught/listen that well, at school, seems convinced they did something clever), or can actually ignore the problems (like Beret Guy). But it could do with streamlining. ''Or'' various brief arguments for and against who is saying it, split up. [[Special:Contributions/172.70.162.161\|172.70.162.161]] 12:35, 4 May 2023 (UTC)		::I read it as someone else, off-panel (traditionall Randall's voice, but not in this case?), who is describing a different time and who clearly didn't/doesn't grasp reality (did not get taught/listen that well, at school, seems convinced they did something clever), or can actually ignore the problems (like Beret Guy). But it could do with streamlining. ''Or'' various brief arguments for and against who is saying it, split up. [[Special:Contributions/172.70.162.161\|172.70.162.161]] 12:35, 4 May 2023 (UTC)
		+	:::I initially (mis?)read “his bank” as reflecting not ownership, but where he banked, but you’re probably right. Either way, the whole thing seems both unclear as to the referents and somewhat misconceived - When a bank pays absurdly high rates, the last thing one would want is to acquire it! [[User:Miamiclay\|Miamiclay]] ([[User talk:Miamiclay\|talk]]) 15:09, 4 May 2023 (UTC)