Suppose that a business provides a continuous income stream with an annual rate of flow at time t given by  f(t) = 120e0.05t  in thousands of dollars per year. If the interest rate is 10% compounded continuously, find the capital value of the business.

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A: The total amount the investor paid is 30×100 = $3000 After two months investor will get from…

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Q: Suppose that the income stream of a business is 12000e0.02t dollars per year for 10 years. At an…

A: Given ft=12000e0.02t rate = r = 4%=0.04

Q: Find the present value for a $90,000 investment for 24 years at a compounded continuously at 4.1%.

A: P=Aert Where P is present value , A is amount and r is rate and t is time.

Q: If $12, 000 is invested at a rate of 3% per year compounded continuously, find value of the…

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Q: Find the present value of a continuous stream of income over 3 years if the rate of income is…

A: Given the rate of income , ft=80e-0.08t Number of yearsT=3 Interest rater=11% The present value can…

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Q: An investment will generate income continuously at the constant rate of $1000 per year for 6 years.…

A: For continuous income stream, we have

Q: Given an interest rate of zero percent, the future value of a lump sum invested today wil always:…

A: Topic = Algebra OA. remain constant, regardless of the investment time period.

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Q: McDonalds estimates it will have a continuous income flow of f(t)= 2510 dollars per year from…

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Q: Find the accumulated present value of an investment over a 8 year period if there is a continuous…

A: We have to find the accumulated present value of an investment.

Q: Find the interest rate needed for an investment of $10,000 to grow to $12,000 in 6 years if interest…

A: Given data: The investment is P=$10000. The final amount is A=$12000. Time taken is t=6 years.

Q: How many years will ittake for an initial investment of $10,000 to grow to $25,000?Assume a rate of…

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Q: How many years are required for an investment to double in value if it is appreciating at the yearly…

A: The final amount when it is compounded continuously is given by  A=P0ert Where r = interest rate…

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Q: The future value that accrues when $400 is invested at 4%, compounded continuously, is S(t) =…

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Q: Find the present value of a continuous stream of income over 3 years when the rate of income is…

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A: I am attaching image so that you understand each and every step.

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Q: Find the accumulated present value of an investment over a 7 year period if there is a continuous…

A: Given, R(t) = 5000 T    = 10 years K    = 2%

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A: Given:

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Q: Find the present value for a $85,000 investment for 11 years at a compounded continuously at 3.2%.

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Q: Suppose you invest R10000 over a period of 6 years. If money is compounded continuously, the annual…

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Q: Find the present value of a continuous stream of income over 4 years when the rate of income is…

A: I have appended the formula used in the solution part of the question.

Q: Find the future value at a rate r, compounded continuously for T years, of a continuous income…

A: To Find the future value, at a rate r, compounded continuously for T years, of a continuous income…

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Q: A company is considering expanding their production capabilities with a new machine that costs…

A: Cost of new machine = 53,000 Investment = 53000 Rate of interest, r= 0.7% per year = 0.007 Time = 9…

Q: uppose that a machine's production can be considered as a continuous income stream with annual rate…

A: Given,A continuous income stream with annual rate of flow at time t is given byf(t( = 10,000 - 800t…

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Q: Suppose that a printing firm considers its production as a continous income stream. If the annual…

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Q: Investment A offers a 8% return compounded semiannually, and investment B offers a 7.81% return…

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Q: Find the present value of a continuous stream of income over 5 years when the rate of income is…

A: On solving this we will get

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.