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, di-vide r into 70.” For instance, an 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.)
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, di-vide r into 70.” For instance, an 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 & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 15T
Related questions
Question
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, di-vide r into 70.” For instance, an 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.)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning