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Question: You decide to start a 401k account. You begin with an initial investment of $5000, and you continuously add to it at a rate of $1000 per year. At the same time, the account accrues interest at a continuous rate of 5% annually. Let V (t) be the value of the account t years after starting it.
(i) Set up a differential equation which describes dV/dt in terms of V .
(ii) This is a separable differential equation. Solve it to get a general formula for V (t). Be sure to keep the necessary constant around.
(iii) Use the initial value to find the constant and get a precise formula for V (t). (iv) When will the 401k be worth $50,000?
1. State five key defining properties of a standard Brownian motion. 2. Outline the advantages and disadvantages of using the continuous time lognormal model for stock prices by considering both the theoretical features of the model and its cons..
The frame around the picture has a uniform width of 2 inches and an area of 96 square inches. What are the dimensions of the picture?
ACCESS TO CAPITAL Refer to Exercise. Milken Institute also ranked the following as the ten worst-performing nations by the ability of their entrepreneurs.
Explain how much more or less the standard deviation of sample means was than the population standard deviation. According to the formula for standard deviation of sample means, it should be far less. (That formula is σ? = σ/√n = σ/√10 = σ/3.1..
Members of an indefinitely large population are either immune to a given disease or are susceptible to it. Let Xn be the number of susceptible members in the population at time period n and suppose X0 = 0 and that in the absence of an epidemic X(n+1)..
A 5.00m X 12.0m swimming pool slopes linearly from a 1.10m depth at one end to a 3.80m depth at the other. What is the volume of the water in the swimming pool?
Confirm that (C ([a, b]) , II·II infinity ) where II f II infinity= max I f (x) I a
Jeremy is saving money to open an indoor skate board park. He needs $10,000 in three years to purchase equipment and initiate a building lease. He's investing his savings in an annuity yielding an annual interest rate of 6.5% compounded monthly.
You just found out that you have been kicked out of your apartment (through no fault of your own!) and need to find a new place to live.
A rectangular trench is to be dug which is to be 180 ft long, 90 ft wide and 8 ft deep. A large dump truck can carry 20 cubic yards in a load. How many truck loads will be required to remove the dirt from this trench?
For a real number x, define r(x) to be the closest integer to x. More precisely, if x ∈ (n - 0.5, n + 0.5]for some n ∈ Z, then r(x) = n. Define the relation ∼ on R by x ∼ y if r(x) = r(y).
Assuming running consumes 99 calories per mile. If you run 8-min miles. What is your average power output, in watts, during a 1 hour run?
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