Assume a 10 Year Period at 8 Compounded Continuously FT 300

Chapter 8

Further Techniques and Applications of Integration - all with Video Answers

Educators


Problem 1

Each of the functions in Exercises $1-14$ represents the rate of flow of money in dollars per year. Assume a 10 -year period at 8$\%$ compounded continuously and find the following: (a) the present value; (b) the accumulated amount of money flow at $t=10$ .
$$f(t)=1000$$

Julian Wong

Julian Wong

Numerade Educator

Problem 2

Each of the functions in Exercises $1-14$ represents the rate of flow of money in dollars per year. Assume a 10 -year period at 8$\%$ compounded continuously and find the following: (a) the present value; (b) the accumulated amount of money flow at $t=10$ .
$$f(t)=300$$

Bobby Barnes

Bobby Barnes

University of North Texas

Problem 3

Each of the functions in Exercises $1-14$ represents the rate of flow of money in dollars per year. Assume a 10 -year period at 8$\%$ compounded continuously and find the following: (a) the present value; (b) the accumulated amount of money flow at $t=10$ .
$$f(t)=500$$

Julian Wong

Julian Wong

Numerade Educator

Problem 4

Each of the functions in Exercises $1-14$ represents the rate of flow of money in dollars per year. Assume a 10 -year period at 8$\%$ compounded continuously and find the following: (a) the present value; (b) the accumulated amount of money flow at $t=10$ .
$$f(t)=2000$$

Bobby Barnes

Bobby Barnes

University of North Texas

Problem 5

Each of the functions in Exercises $1-14$ represents the rate of flow of money in dollars per year. Assume a 10 -year period at 8$\%$ compounded continuously and find the following: (a) the present value; (b) the accumulated amount of money flow at $t=10$ .
$$f(t)=400 e^{0.03 t}$$

Julian Wong

Julian Wong

Numerade Educator

Problem 6

Each of the functions in Exercises $1-14$ represents the rate of flow of money in dollars per year. Assume a 10 -year period at 8$\%$ compounded continuously and find the following: (a) the present value; (b) the accumulated amount of money flow at $t=10$ .
$$f(t)=800 e^{0.05 t}$$

Bobby Barnes

Bobby Barnes

University of North Texas

Problem 7

Each of the functions in Exercises $1-14$ represents the rate of flow of money in dollars per year. Assume a 10 -year period at 8$\%$ compounded continuously and find the following: (a) the present value; (b) the accumulated amount of money flow at $t=10$ .
$$f(t)=5000 e^{-0.01 t}$$

Julian Wong

Julian Wong

Numerade Educator

Problem 8

Each of the functions in Exercises $1-14$ represents the rate of flow of money in dollars per year. Assume a 10 -year period at 8$\%$ compounded continuously and find the following: (a) the present value; (b) the accumulated amount of money flow at $t=10$ .
$$f(t)=1000 e^{-0.02 t}$$

Bobby Barnes

Bobby Barnes

University of North Texas

Problem 9

Each of the functions in Exercises $1-14$ represents the rate of flow of money in dollars per year. Assume a 10 -year period at 8$\%$ compounded continuously and find the following: (a) the present value; (b) the accumulated amount of money flow at $t=10$ .
$$f(t)=25 t$$

Julian Wong

Julian Wong

Numerade Educator

Problem 10

Each of the functions in Exercises $1-14$ represents the rate of flow of money in dollars per year. Assume a 10 -year period at 8$\%$ compounded continuously and find the following: (a) the present value; (b) the accumulated amount of money flow at $t=10$ .
$$f(t)=50 t$$

Bobby Barnes

Bobby Barnes

University of North Texas

Problem 11

Each of the functions in Exercises $1-14$ represents the rate of flow of money in dollars per year. Assume a 10 -year period at 8$\%$ compounded continuously and find the following: (a) the present value; (b) the accumulated amount of money flow at $t=10$ .
$$f(x)=0.02 x+300$$

Julian Wong

Julian Wong

Numerade Educator

Problem 12

Each of the functions in Exercises $1-14$ represents the rate of flow of money in dollars per year. Assume a 10 -year period at 8$\%$ compounded continuously and find the following: (a) the present value; (b) the accumulated amount of money flow at $t=10$ .
$$f(t)=0.05 t+500$$

Bobby Barnes

Bobby Barnes

University of North Texas

Problem 13

Each of the functions in Exercises $1-14$ represents the rate of flow of money in dollars per year. Assume a 10 -year period at 8$\%$ compounded continuously and find the following: (a) the present value; (b) the accumulated amount of money flow at $t=10$ .
$$f(t)=1000 t-100 t^{2}$$

Julian Wong

Julian Wong

Numerade Educator

Problem 14

Each of the functions in Exercises $1-14$ represents the rate of flow of money in dollars per year. Assume a 10 -year period at 8$\%$ compounded continuously and find the following: (a) the present value; (b) the accumulated amount of money flow at $t=10$ .
$$f(t)=2000 t-150 t^{2}$$

Bobby Barnes

Bobby Barnes

University of North Texas

Problem 15

Accumulated Amount of Money Flow John deposited his money in a bank that gives a continuous rate of flow of money of $\$ 10,000$ per year for 5 years. Find the accumulated amount at an interest rate of 2$\%$ compounded continuously.

Julian Wong

Julian Wong

Numerade Educator

Problem 16

Present Value An investment is expected to produce a uniform continuous rate of money flow of $\$ 2000$ per year for 2 years. Find the present value at the following rates, compounded continuously
(a) 3$\%$ (b) 6$\%$ (c) 9$\%$

Bobby Barnes

Bobby Barnes

University of North Texas

Problem 17

Money Flow The rate of a continuous flow of money starts at $\$ 5000$ and decreases exponentially at 1$\%$ per year for 8 years. Find the present value and final amount at an interest rate of 8$\%$ compounded continuously.

Julian Wong

Julian Wong

Numerade Educator

Problem 18

Money Flow The rate of a continuous money flow starts at $\$ 1000$ and increases exponentially at 5$\%$ per year for 4 years. Find the present value and accumulated amount if interest earned is 3.5$\%$ compounded continuously.

Bobby Barnes

Bobby Barnes

University of North Texas

Problem 19

Present Value A money market fund has a continuous flow of money at a rate of $f(t)=1500-60 t^{2}$ , reaching 0 in 5 years. Find the present value of this flow if interest is 5$\%$ compounded continuously.

Julian Wong

Julian Wong

Numerade Educator

Problem 20

Accumulated Amount of Money Flow Find the amount of a continuous money flow in 3 years if the rate is given by $f(t)=1000-t^{2}$ and if interest is 5$\%$ compounded continuously.

Bobby Barnes

Bobby Barnes

University of North Texas

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