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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 5.4, Problem 68E
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Finding the Amount of an Annuity In Exercises 67-70, find the amount of an annuity with income function C(t), interest rate r, and term T. See Example 9.

c ( t ) = $ 1500 ,   r = 7 % , T = 4  years

To determine

To calculate: The amount of an annuity with income function c(t)=$500,r=7% and T=4 years.

Explanation

Given Information:

The amount of an annuity with income function c(t)=$500,r=7% and T=4 years.

Formula used:

If c represents a continuous income function in dollars per year (where t is the time in years),

r Represents the interest rate (in decimal form) compounded continuously, and T represents the term of the annuity in years, then the amount of annuity is,

erT∫0Tc(t)e−rtdt

Calculation:

The income function for your deposit is c(t)=$500.

So, the amount of the annuity after 4 years will be

erT∫0Tc(t)e−rtdt

Now, substitute c(t)=$500,r=

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