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.
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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
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