Most savings banks advertise that they compound interest continuously, meaning that the amount S(t) in an account satisfies the differential equation ds/dt=rS, where is the annual interest rate and t is time measured in years.Show that an annual interest rate of 8% compounded continuously is the same as an annual interest rate of 8.33% compounded in years. Show that an annual interest rate of r compounded continuously is the same as an annual interest rate of e^r-1 compounded annually.

Answered: Image /qna-images/answer/5ab25bde-0334-490f-bf97-1f750a2758d1.jpg

Answered: Most savings banks advertise that they…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Concept explainers

Question

Most savings banks advertise that they compound interest continuously, meaning that the amount S(t) in an account satisfies the differential equation ds/dt=rS, where is the annual interest rate and t is time measured in years.

Show that an annual interest rate of 8% compounded continuously is the same as an annual interest rate of 8.33% compounded in years.
Show that an annual interest rate of r compounded continuously is the same as an annual interest rate of e^r-1 compounded annually.

Expert Solution

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated