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5. Suppose that a sum So is invested at an annual rate of return r compounded continuously. a. Find the time T required for the original sum to double in volue

5. Suppose that a sum So is invested at an annual rate of return r compounded continuously. a. Find the time T required for the original sum to double in volue

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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t e S y A(h) dh dt equation = 301 ut -aa√/2gh, (34) where A(h) is the area of the cross section of the tank at height h and a is the area of the outlet. The constant a is a contraction coefficient that accounts for the observed fact that the cross section of the (smooth) outflow stream is smaller than a. The value of a for water is about 0.6. c. Consider a water tank in the form of a right circular cylinder that is 3m high above the outlet. The radius of the tank is 1m, and the radius of the circular outlet is 0.1 m. If the tank is initially full of water, determine how long it takes to drain the tank down to the level of the outlet. 5. Suppose that a sum So is invested at an annual rate of return r compounded continuously. a. Find the time T required for the original sum to double in value as a function of r. b. Determine T if r = 7%. c. Find the return rate that must be achieved if the initial investment is to double in 8 years. 6. A young person with no initial capital invests k dollars per year at an annual rate of return r. Assume that investments are made continuously and that the return is compounded continuously. a. Determine the sum S(t) accumulated at any time t. b. If r = 7.5%, determine k so that $1 million will be available for retirement in 40 years. c. If k = $2000/year, determine the return rate r that must be obtained to have $1 million available in 40 years.
Transcribed Image Text:t e S y A(h) dh dt equation = 301 ut -aa√/2gh, (34) where A(h) is the area of the cross section of the tank at height h and a is the area of the outlet. The constant a is a contraction coefficient that accounts for the observed fact that the cross section of the (smooth) outflow stream is smaller than a. The value of a for water is about 0.6. c. Consider a water tank in the form of a right circular cylinder that is 3m high above the outlet. The radius of the tank is 1m, and the radius of the circular outlet is 0.1 m. If the tank is initially full of water, determine how long it takes to drain the tank down to the level of the outlet. 5. Suppose that a sum So is invested at an annual rate of return r compounded continuously. a. Find the time T required for the original sum to double in value as a function of r. b. Determine T if r = 7%. c. Find the return rate that must be achieved if the initial investment is to double in 8 years. 6. A young person with no initial capital invests k dollars per year at an annual rate of return r. Assume that investments are made continuously and that the return is compounded continuously. a. Determine the sum S(t) accumulated at any time t. b. If r = 7.5%, determine k so that $1 million will be available for retirement in 40 years. c. If k = $2000/year, determine the return rate r that must be obtained to have $1 million available in 40 years.
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