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If $\$ 5000$ is deposited into an account for 8 years and earns interest at $4.75 \%$ compounded continuously, find the average value of the account during the 8 year period.

$$\$ 6082.69$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 7

Substitution and Properties of Definite Integrals

Integrals

Campbell University

Baylor University

Idaho State University

Boston College

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

03:06

Suppose you deposit $6000 …

01:19

Find the interest earned o…

01:36

Present Value Find the pre…

01:02

okay for this problem we're using the compound interest formula continuously compounded interest. So we have B equals P E to the R T. So we can start by finding the ending balance. Be by substituting $50,000 in for P and six in for our or six in for tea and 60.0 for 1 to 5 in for our four in an eighth is the same as 4.1 to 5, and then we divide that by 100 to change it into a decimal. Now, when you're putting this in your calculator, make sure that both of these numbers end up in the exponents and you'll get a final balance of $64,040.97. But the question is how much interest was earned, not what is the final balance. So we need to subtract the original $50,000 from this, and the amount of interest is $14,040.97

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