The rule of 72 for compound interest | Interest and debt | Finance & Capital Markets | Khan Academy

Using the Rule of 72 to approximate how long it will take for an investment to double at a given interest rate. Created by Sal Khan. Watch the next lesson: https://www.khanacademy.org/economics-finance-domain/core-finance/interest-tutorial/interest-basics-tutorial/v/introduction-to-interest?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets Missed the previous lesson? Watch here: https://www.khanacademy.org/economics-finance-domain/core-finance/interest-tutorial/compound-interest-tutorial/v/introduction-to-compound-interest?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets Finance and capital markets on Khan Academy: Interest is the basis of modern capital markets. Depending on whether you are lending or borrowing, it can be viewed as a return on an asset (lending) or the cost of capital (borrowing). This tutorial gives an introduction to this fundamental concept, including what it means to compound. It also gives a rule of thumb that might make it easy to do some rough interest calculations in your head. About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1 Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

Comments

1. Thank you so much
2. Rule of 69 huh. ( ͡° ͜ʖ ͡°)
3. how to triple the money, if interest 10%
4. hahahaha this was amazingly cool and useful😎
5. can you use this rule to estimate how long it will take investments to double with interest compounded semi-annual or quarterly ?
6. rule of 69. puts on sun glasses
7. great
8. 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?
9. 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. ???
10. nice shortcut
11. 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 ?
12. Thank you
13. I Just wanted help on year 10 maths homework.....then it all got hard
14. i think log 1.01 not 1.1 at 1% interest
15. 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
16. For those who are wondering where the 69 and 72 numbers come in, it's from taking the first term of a Taylor series expansion. Details on http://web.stanford.edu/class/ee204/TheRuleof72.html
17. I'm totally watching all these videos 3 hours before my finals... I am starting to finally grasp the idea finally. Thanks!
18. what would you do for tripling or continuously compounding?
19. 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<x<.2, we can see roughly that 69<y<76. If you take the very middle of this range you get 72.5, so we could use 72 or 73 and get pretty close for reasonable values of x.
20. 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..."