Homework Help is Here – Start Your Trial Now!
Math
Calculus
66. The Rule of 70 A well-known rule in the world of finance is that an annual interest rate of R% will double an investment in approximately 70/R years. Assume that the money is com- pounded continuously so that you can use the Pen formula. (a) Solve the equation Pe" = 2P to find t as a function of r. (b) If r = R%, write t as a function of R. (c) If the money is not compounded continuously, the dou- bling time will be a little longer than the answer in (b). Approximate the typical doubling time by increasing the numerator by 1. This should explain the Rule of 70!

66. The Rule of 70 A well-known rule in the world of finance is that an annual interest rate of R% will double an investment in approximately 70/R years. Assume that the money is com- pounded continuously so that you can use the Pen formula. (a) Solve the equation Pe" = 2P to find t as a function of r. (b) If r = R%, write t as a function of R. (c) If the money is not compounded continuously, the dou- bling time will be a little longer than the answer in (b). Approximate the typical doubling time by increasing the numerator by 1. This should explain the Rule of 70!

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
icon
Related questions
Question
66. The Rule of 70 A well-known rule in the world of finance is that an annual interest rate of R% will double an investment in approximately 70/R years. Assume that the money is com- pounded continuously so that you can use the Pe" formula. (a) Solve the equation Pet = 2P to find t as a function of r. (b) If r = R%, write t as a function of R. (c) If the money is not compounded continuously, the dou- bling time will be a little longer than the answer in (b). Approximate the typical doubling time by increasing the numerator by 1. This should explain the Rule of 70!
Transcribed Image Text:66. The Rule of 70 A well-known rule in the world of finance is that an annual interest rate of R% will double an investment in approximately 70/R years. Assume that the money is com- pounded continuously so that you can use the Pe" formula. (a) Solve the equation Pet = 2P to find t as a function of r. (b) If r = R%, write t as a function of R. (c) If the money is not compounded continuously, the dou- bling time will be a little longer than the answer in (b). Approximate the typical doubling time by increasing the numerator by 1. This should explain the Rule of 70!
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS