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(a) Find the present value of $\$ 8,000$ per year flowing uniformly over a 20 year period if it earns $6 \%$ interest compounded continuously. (b) What is its final value?

(a) $\$ 93,174,11$(b) $\$ 309,348.92$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 8

Applications of the Definite Integral

Integrals

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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.

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in this problem were given a uniform continuous rate of money flow of $8000 a six year period. We were asked to find the present value at the following interest rates. The equation for present value is P equals Thean a girl, eh 50 e to the negative rt d t from zero to capital t. We can use this to find our present values. Given the certain interest rates three time, all we have to change is our our value. We know that f of tea is going to be our 8000. We can fill in those numbers, So this is gonna be the base part of our equation. In case I didn't mention it before. This six is our six years. So for part A, we have an interest rate of 2%. We're gonna fill in a to for the whore. Then we're going to evaluate that. So once evaluated, you should have a president value $45,231.80. Next we're gonna change are too to a five. That's the next interest rate that were asked about. And then we're going to evaluate that in a girl once evaluated your present value before you $1469 in 10 cents. Finally, we can replace our five within eight and evaluate that in a girl. So once evaluated, your president value should be $38,121.70.

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