   Chapter 5, Problem 85RE ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Compound Interest A deposit of $500 is made in a savings account at an annual interest rate of 4%, compounded continuously. Find the average balance in the account during the first 6 years. To determine To calculate: The average balance after 6 years in an account if deposit of$500 made in a savings account where the interest rate is 4% annually compounded continuously.

Explanation

Given information:

A deposit of $500 made in a savings account. The interest rate is 4% annually. Formula used: The average value of a provided function can be calculated as, Average value=1baabf(x)dx Where f is a continuous function in the interval [a,b]. Calculation: The deposit is$500, interest rate is 4% and time is 6 years. The function is defined as,

f(t)=Aert

Here, r is the interest rate and A is the deposit amount.

Substitute r=0.04 and A=500 in the above equation. So,

f(t)=500e0.04t

Substitute b for 6, a for 0 in the average value formula as shown below,

1baabf(x)dx=16006500e0

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