Chapter 5.4, Problem 67E

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

Chapter
Section

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 ) = $250 , r = 8 % , T = 6 years To determine To calculate: The amount of an annuity with income function c(t)=$250,r=8%, and T=6 years.

Explanation

Given Information:

The amount of an annuity with income function c(t)=$250,r=8%, and T=6 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, erT0Tc(t)ertdt Calculation: The income function for your deposit is c(t)=$250.

So, the amount of the annuity after 6 years will be

erT0Tc(t)ertdt

Now, substitute c(t)=250,r=0

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