×
Log in to StudySoup
Get Full Access to Math - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Math - Textbook Survival Guide

Many savings banks now advertise continuous compounding of interest. This means that the

Differential Equations and Their Applications: An Introduction to Applied Mathematics | 3rd Edition | ISBN: 9780387908069 | Authors: M. Braun ISBN: 9780387908069 381

Solution for problem 19 Chapter 1.8

Differential Equations and Their Applications: An Introduction to Applied Mathematics | 3rd Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
Differential Equations and Their Applications: An Introduction to Applied Mathematics | 3rd Edition | ISBN: 9780387908069 | Authors: M. Braun

Differential Equations and Their Applications: An Introduction to Applied Mathematics | 3rd Edition

4 5 1 387 Reviews
30
0
Problem 19

Many savings banks now advertise continuous compounding of interest. This means that the amount of money P(t) on deposit at time t, satisfies the differential equation dP(r)/dt = rP(t) where r is the annual interest rate and r is measured in years. Let Po denote the original principal. (a) Show that P (I)= Poer. (b) Let r = 0.0575, 0.065, 0.0675, and 0.075. Show that er= 1.05919, 1.06716, 1.06983, and 1.07788, respectively. Thus, the effective annual yield on interest rates of 5$, 6f, 65, and 7t% should be 5.919, 6.716, 6.983, and 7.788% respectively. Most banks, however, advertise effective annual yields of 6, 6.81, 7.08, and 7.9%, respectively. The reason for this discrepancy is that banks calculate a daily rate of interest based on 360 days, and they pay interest for each day money is on deposit. For a year, one gets five extra days. Thus, we must multiply the annual yields of 5.919, 6.716, 6.983, and7.788% by 365/360, and then we obtain the advertised values.(c) It is interesting to note that the Old Colony Cooperative Bank in Rhode Islandadvertises an effective annual yield of 6.72% on an annual interest rateof 6f% (the lower value), and an effective annual yield of 7.9% on an annualinterest rate of 7;%. Thus they are inconsistent.

Step-by-Step Solution:
Step 1 of 3

PROJECT: mulching trees, debris removal Project Confirmation Each participant should bring: Thank you for volunteering to help with the Deboer Park • Liability waiver Project! Details for the day are as follows: • Work gloves Daate:Occtober...

Step 2 of 3

Chapter 1.8, Problem 19 is Solved
Step 3 of 3

Textbook: Differential Equations and Their Applications: An Introduction to Applied Mathematics
Edition: 3
Author: M. Braun
ISBN: 9780387908069

The answer to “Many savings banks now advertise continuous compounding of interest. This means that the amount of money P(t) on deposit at time t, satisfies the differential equation dP(r)/dt = rP(t) where r is the annual interest rate and r is measured in years. Let Po denote the original principal. (a) Show that P (I)= Poer. (b) Let r = 0.0575, 0.065, 0.0675, and 0.075. Show that er= 1.05919, 1.06716, 1.06983, and 1.07788, respectively. Thus, the effective annual yield on interest rates of 5$, 6f, 65, and 7t% should be 5.919, 6.716, 6.983, and 7.788% respectively. Most banks, however, advertise effective annual yields of 6, 6.81, 7.08, and 7.9%, respectively. The reason for this discrepancy is that banks calculate a daily rate of interest based on 360 days, and they pay interest for each day money is on deposit. For a year, one gets five extra days. Thus, we must multiply the annual yields of 5.919, 6.716, 6.983, and7.788% by 365/360, and then we obtain the advertised values.(c) It is interesting to note that the Old Colony Cooperative Bank in Rhode Islandadvertises an effective annual yield of 6.72% on an annual interest rateof 6f% (the lower value), and an effective annual yield of 7.9% on an annualinterest rate of 7;%. Thus they are inconsistent.” is broken down into a number of easy to follow steps, and 212 words. This textbook survival guide was created for the textbook: Differential Equations and Their Applications: An Introduction to Applied Mathematics, edition: 3. The full step-by-step solution to problem: 19 from chapter: 1.8 was answered by , our top Math solution expert on 03/13/18, 07:00PM. Since the solution to 19 from 1.8 chapter was answered, more than 213 students have viewed the full step-by-step answer. This full solution covers the following key subjects: . This expansive textbook survival guide covers 65 chapters, and 855 solutions. Differential Equations and Their Applications: An Introduction to Applied Mathematics was written by and is associated to the ISBN: 9780387908069.

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

Many savings banks now advertise continuous compounding of interest. This means that the

×
Log in to StudySoup
Get Full Access to Math - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Math - Textbook Survival Guide
×
Reset your password