You can show that 72 is a good approximation by looking at what number y satisfies the relationship log(2)/log(1+x) = y/100x, where x is the decimal representation of the percentage. Solving this gives y=100log(2)x/log(1+x), and restricting x values to reasonable interest rates, 0
The rule of 69 is probably more fun when using logs. But complexity aside -- if simple interest means it takes 10 years to double $100 at 10%. And now we know the rule of 72 -- then it takes 7.2 years to double with compound interest. IT is that simple. 10 years at simple interest to double 7.2 years at compound interest NOW i can do it in my head and approximate other interest values. So why all the COMPLEXITY. ???
@@nee7427 Oh man... If I recall, this was for my 1030 class, and I failed. I had to convince my professor to raise my grade and she let me retake one more exam and she would replace my lowest score with that exam result. Thankfully passed with D+ after!
It's actually the "Rule of 69" but using 70 or 72 makes the calculation easier with some loss of accuracy. This is continuous compounding but banks etc. might apply less frequent compounding periods such as months or years. Handy as a quick mental arithmetic method - it is a consequence of exponential growth as ln(2) = 0.69315... or 69% approx.
It works with both. ln(2)/ln(1.1) = 0.693/0.0953 = 7.27 You just need to use the same base for the numerator and the denominator. Sal hints at this at 4:23 when he says "x should equal to log base anything really 2..."
Use your N, I, PV, FV functions on your financial calculator. So $100 is PV or principal, time is what you solve for with his equation for N 7.2 in this case, and plug in the interest for I 10%, then hit FV to get what it is worth which for me was -198.62 or roughly $200. Hitting the (+/-) key when entering PV will make the -198.62 positive. Really late answer, sorry man!
Interesting stuff, but doing the actual math really is not that much harder. I suppose if you have to do everything in your head this makes sense, but I don't know when you would need to make any sort of financial decision/calculation without access to a calculator (you can do all calculations necessary in the calculator app on your phone).
True or False: hypothetically if you made a ridiculous amount of profit on your investment it could be more beneficial for you to invest in a regular capital investment over an Ira being that the taxes on the capital investment are only 15 % as opposed to 25% when you are retired
It's actually pretty easy. The Rule of 72 literally means that you divide 72 by the interest rate. Let's say you have an interest rate of 4%, and you use this to divide 72 with. The answer would be 18, so, it would say that it would take you 18 years to double your money. The higher the interest rates, the lesser the years it would take you to double your money.
rule of 69. *puts on sun glasses*
You can show that 72 is a good approximation by looking at what number y satisfies the relationship log(2)/log(1+x) = y/100x, where x is the decimal representation of the percentage. Solving this gives y=100log(2)x/log(1+x), and restricting x values to reasonable interest rates, 0
The rule of 69 is probably more fun when using logs.
But complexity aside -- if simple interest means it takes 10 years to double $100 at 10%.
And now we know the rule of 72 -- then it takes 7.2 years to double with compound interest. IT is that simple.
10 years at simple interest to double
7.2 years at compound interest
NOW i can do it in my head and approximate other interest values. So why all the
COMPLEXITY. ???
ummm lol
I'm totally watching all these videos 3 hours before my finals... I am starting to finally grasp the idea finally. Thanks!
How was your exam ? :P
@@nee7427 Oh man... If I recall, this was for my 1030 class, and I failed. I had to convince my professor to raise my grade and she let me retake one more exam and she would replace my lowest score with that exam result. Thankfully passed with D+ after!
@@toothpickvideos94 didn't expect an reply 😂
Thanks anyway 😁
It is difficult to figure out which the next video is, related to previous. Could you please arrange them in order?
It's actually the "Rule of 69" but using 70 or 72 makes the calculation easier with some loss of accuracy. This is continuous compounding but banks etc. might apply less frequent compounding periods such as months or years. Handy as a quick mental arithmetic method - it is a consequence of exponential growth as ln(2) = 0.69315... or 69% approx.
nice
Nice
nice
It works with both. ln(2)/ln(1.1) = 0.693/0.0953 = 7.27
You just need to use the same base for the numerator and the denominator.
Sal hints at this at 4:23 when he says "x should equal to log base anything really 2..."
very enlightening. thank you
Sal takes my breath away.
No, the rule of 69 has nothing to do with math, lad.
Thank you
So does the rule of 72 only apply when it's doubling the amount? It doesn't work if it's triple or quadruple?
I Just wanted help on year 10 maths homework.....then it all got hard
this person is 21 now, woah
Could this work for continuous too or simply just annual
It's cute how he really wanted to do just another one "for fun" °=°
What the 72 suppose to be the input money?
hahahaha this was amazingly cool and useful😎
Log. ln is a natural log, which is base e. Log is base 10. You want log for this.
what would you do for tripling or continuously compounding?
you dont.
Thank you so much
Can someone tell me what to do...if they give you The PRINCIPAL, the TIME and and the FINAL VALUE but not the Interest rate?
Use your N, I, PV, FV functions on your financial calculator. So $100 is PV or principal, time is what you solve for with his equation for N 7.2 in this case, and plug in the interest for I 10%, then hit FV to get what it is worth which for me was -198.62 or roughly $200. Hitting the (+/-) key when entering PV will make the -198.62 positive. Really late answer, sorry man!
rambow70 Oh it's fine I got it sorted. Thanks so much for the answer anyways 😃
can you use this rule to estimate how long it will take investments to double with interest compounded semi-annual or quarterly ?
No
No, take note that in this rule, it is a yearly calculation and estimation. This rule goes a long way anyway if you're knowledgeable enough.
If i invest 5000 per month for 10years and annual return would be 8%, how much i will be getting at the end of policy term ?
nice shortcut
Interesting stuff, but doing the actual math really is not that much harder. I suppose if you have to do everything in your head this makes sense, but I don't know when you would need to make any sort of financial decision/calculation without access to a calculator (you can do all calculations necessary in the calculator app on your phone).
what happens when the compounding period is changed to monthly for example, will the percentage change or not?
I believe you would have the same value, mate. Whether if it's annually or monthly.
great
True or False: hypothetically if you made a ridiculous amount of profit on your investment it could be more beneficial for you to invest in a regular capital investment over an Ira being that the taxes on the capital investment are only 15 % as opposed to 25% when you are retired
I was actually guessing it would be around 8 before you used the calculator . I feel kinda smarts :)
*smart, not very smart eh?
@@SabrinaXe bruh savage, lmao this is 2 years ago
how to triple the money, if interest 10%
are you a wizard?
Here I was thinking the meaning of life was 42?
rule of 69
me:heh heh 69
I'm too dumb for this man.
It's actually pretty easy. The Rule of 72 literally means that you divide 72 by the interest rate. Let's say you have an interest rate of 4%, and you use this to divide 72 with. The answer would be 18, so, it would say that it would take you 18 years to double your money. The higher the interest rates, the lesser the years it would take you to double your money.
rule of 69 heheehhe
Thank you