For the differential equation model obtained in Problem 5, find Q(t) by separating the variables and integrating.

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For the differential equation model obtained in Problem 5, find Q(t) by separating the variables and integrating.

a. Evaluate Q (1).

b. Compare your previous estimates of Q (1) with its actual value.

c. Find the effective annual interest rate when an annual rate of 10% is compounded continuously.

d. Compare the effective annual interest rate computed in part (c) with interest compounded.

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Data from problem 5

When interest is compounded, the interest earned is added to the principal amount so that it may also earn interest. For a 1-year period, the principal amount Q is given by:

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where i is the annual interest rate (given as a decimal) and n is the number of times during the year that the interest is compounded. To lure depositors, banks offer to compound interest at different intervals: semiannually, quarterly, or daily. A certain bank advertises that it compounds interest continuously. If $100 is deposited initially, formulate a mathematical model describing the growth of the initial deposit during the first year. Assume an annual interest rate of 10%.

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A First Course In Mathematical Modeling

ISBN: 9781285050904

5th Edition

Authors: Frank R. Giordano, William P. Fox, Steven B. Horton

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