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

ISBN: 9780387908069 381

## Solution for problem 19 Chapter 1.8

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

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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.

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##### 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.

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