Two investments, A and B, produce a continuous income stream of 3%, compounded continuously. The rate of flow of income from investment A is f(t) = 3000e0.04t and the rate of flow of income from investment B is expected to be g(t) = 5000. (a) Find the total income produced by each of the two investments over the 7-year period. (b) Find the future value, the accumulated amount of money flow, of each of the two investments for 7 years. (c) Compute the interest earned by each investment over the 7-year period. (d) Find the present value of each of the two investments. (e) Interpret the answers determined in (a) to (d)

Q: Suppose stock A is priced at $30/share and the company will pay a dividend of $0.30/share after two…

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

Q: man wished to have a p 40,000 in certain fund at the end of 8 years that will pay a nominal rate of…

A: Given query is to find compund amount factor

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: A 35-year-old teacher is offered an opportunity to invest some money in a retirement account that…

A: As per our guidelines, we can answer one question only. please repost other seperately.

Q: Find the future value P of the amount Po invested for time period t at interest rate k, compounded…

A:

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

A:

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: A small company is trying to decide whether or not to upgrade its website. The upgrade costs 5,000,…

A: Given:-               A small company is trying to decide whether or not to upgrade its website.…

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.

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

A: SOLUTION-

Q: A car washing machine is expected to generate $40,000 in revenue per year, for the next 5 years. If…

A:

Q: A saving account deposit of $150 is to earn 6.5% compounded continuously. What amount should have…

A: Use the formula for the compound interest and substitute the given values than simplify.

Q: Suppose income from an endowment is generated at the annual rate of $42,000 per year. Find the…

A: Given: The annual rate of $42,000 per year, an interest rate of 7.5% compounded continuously. Find:…

Q: Find the capital value of a fort at a strategic location, where the annual rent is $950,000, paid in…

A: Given that the annual rent of a fort at a strategic location is $950,000 with the compound interest…

Q: The proceeds from the sale of a building will yield a uniform continuous flow of $10,000 a year for…

A:

Q: A recently installed machine earns the company revenue at a continuous rate of 60,000t + 45,000…

A: (a) We have to find the present value of the revenue earned by the machine during the first year of…

Q: A car washing machine is expected to generate $40,000 in revenue per year, for the next 5 years. If…

A:

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

A:

Q: Leonard's current salary is $65,000. Ten years from now, how much will he need to earn to retain his…

A: Given information Present annual salaryP=$65,000 Rate of inflationr=3% per year compounded…

Q: Find the present value of a continuous income stream F(t)=30+5t, where t is in years and F is in…

A:

Q: If $P is invested for n years at 10% compounded continuously, the future value that results after n…

A:

Q: suppose that r(t)=250,000 is a continuous income stream for 5 years at 5% compounded continuously.…

A: Given query is to find the future value of the income stream.

Q: Find the present value Po of each amount P due t years in the future and invested at interest rate…

A: Given: The amount P= $100,000 The time is t= 6 years. The rate of interest is k=3%

Q: An investor has $10000 to invest in either a bond that matures in 5 years or a business that will…

A:

Q: An initial amount of $1800 is invested in an account at an interest rate of 3.5% per year,…

A: givenP=$1800r=3.5%=0.035t=7 yearssince we are solving compouded continuously ,then we apply this…

Q: Find the present value of a continuous stream of income over 2 years when the rate of income is…

A:

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

A:

Q: 7. At what interest rate compounded continuously must money be invested in order to triple in 10…

A: We know that  P=Aert where A= Principal value r=rate  and t=time

Q: Find the capital value of a fort at a strategic location, where the annual rent is $750,000, paid in…

A:

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

A: Given, Rate of income per year is $35000. Interest rate is 4%. Here we shall use the formula for…

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: An investor is looking at an income stream of the form F(t) = 1+e¬0.2t (in some multiple of dollars…

A: the cash flow is given by the function  and the interest rate is 1.5% compounded continuously so…

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…

Q: Suppose that a donor wishes to provide a cash gift to a hospital that will generate a continuous…

A: Given:- From the question , the annual rate of flow of the continuous income stream per year is ft=$…

Q: What initial investment at 8% compounded continuously for 5 years will accumulate to $50, 000?

A:

Q: In the future value of $1000 invested for n years at 12%, compounded continuously, is given by S=…

A:

Q: A new restaurant is expected to produce a continuous income stream at the rate of R(t) = 100,000…

A: Here the present income R(t)=100000 Interest rate (r)=4% Time(t)=5 year The income stream is…

Q: Following the birth of a​ child, a parent wants to make an initial investment P0 that will grow to…

A: detailed solution is given below

Q: The parents of a 3-year-old child put $10,000 into an account with the hope that the amount will…

A:

Q: continuous income stream has an annual rate of flow at time t given by f(t) = 12,000e0.04t…

A: Explanation and solutions is given below.....

Q: How long does it take to have a balance of $900 if $500 is invested at 0.75% annual interest…

A:

Q: An initial amount of $1800 is invested in an account at an interest rate of 7% per year, compounded…

A:

Q: A car washing machine is expected to generate $40,000 in revenue per year, for the next 5 years. If…

A:

Q: Adrian is going to invest $9,900 and leave it in an account for 10 years. Assuming the interest is…

A: Simply use the formula for compound interest.

Q: 2) Bank A offers 5% nominal interest compounded every 3 months. What is the nominal interest rate…

A: Given that, Bank A offers 5% nominal interest compounded every 3 months.

Q: The future value at 7​% ​interest compounded continuously for 5 ​years, of the continuous income…

A:

Q: how long will it take to have a final balance of $100,000 if $1,000 is invested at 5% interest rate…

A:

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

A: The formula for compound interest on an investment of P amount at an r% interest rate is A =…

Q: Calculate the present value PV of an investment that will be worth $1,000 at the stated interest…

A:

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.