Chapter 12.3, Problem 49E

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Chapter
Section

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

Compound interest If $P is invested for n years at 10 % compounded continuously, the rate at which the future value is growing is d S d n = 0.1 P e 0.1 n (a) To determine To calculate: The future value at the end of n years when an amount of$P is invested for n years at 10% compounded continuously and the rate at which the future value is growing as:

dSdn=0.1Pe0.1n.

Explanation

Given Information:

An amount of $P is invested for n years at 10% compounded continuously, the rate at which the future value is growing as dSdn=0.1Pe0.1n Formula used: The logarithm formula is u1u'dx=u'udu=ln|u|+C where u is a function of x. Calculation: Consider that if$P is invested for n years at 10% compounded continuously, the rate at which the future value is growing is

dSdn=0

(b)

To determine

To calculate: The number of years after which the future value will double when an amount of \$P is invested for n years at 10% compounded continuously and the rate at which the future value is growing as dSdn=0.1Pe0.1n.

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