The rule of 70 If you use the approximation ln 2 0.70 (in place of 0.69314c), you can derive a rule of thumb that says, “To estimate how many years it will take an amount of money to double when invested at r percent compounded continuously, divide r into 70.” For instance, the amount of money invested at 5% will double in about 70/5 = 14 years. If you want it to double in 10 years instead, you have to invest it at 70/10 = 7%. Show how the rule of 70 is derived. (A similar “rule of 72” uses 72 instead of 70, because 72 has more integer factors.)
The rule of 70 If you use the approximation ln 2 0.70 (in place of 0.69314c), you can derive a rule of thumb that says, “To estimate how many years it will take an amount of money to double when invested at r percent compounded continuously, divide r into 70.” For instance, the amount of money invested at 5% will double in about 70/5 = 14 years. If you want it to double in 10 years instead, you have to invest it at 70/10 = 7%. Show how the rule of 70 is derived. (A similar “rule of 72” uses 72 instead of 70, because 72 has more integer factors.)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter4: Exponential And Logarithmic Functions
Section4.CT: Chapter Test
Problem 11CT
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The rule of 70 If you use the approximation ln 2 0.70 (in place of 0.69314c), you can derive a rule of thumb that says, “To estimate how many years it will take an amount of money to double when invested at r percent compounded continuously, divide r into 70.” For instance, the amount of money invested at 5% will double in about 70/5 = 14 years. If you want it to double in 10 years instead, you have to invest it at 70/10 = 7%. Show how the rule of 70 is derived. (A similar “rule of 72” uses 72 instead of 70, because 72 has more integer factors.)
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