Suppose that a machine's production can be considered as a continuous income stream with annual rate of flow at time t given by f(t) = 10,000 − 900t (dollars per year). If money is worth 10%, compounded continuously, find the present value of the machine over the next 8 years.

Q: If $4,000 is invested at 7% compounded continuously, how long will it take for it to grow to $6,000,…

A:

Q: Find the interest earned at 5% compounded continuously for 2 years by a continuous income stream…

A: Given the interest earned r=5%=0.05 , t=2years and PV=1250. We have to find the interest.

Q: 4. How much should be invested at 12.5% compounded continuously to end up with $1000 at the end of 5…

A:

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: Find the amount resulting in 12 years, if $25,000 is invested now at an interest rate of 4.25% p.a.…

A: Given that, P=25000, r=4.25%, t=12years

Q: 3. How long will it take $5000 to triple if it is invested at 7.5% compounded continuously?

A:

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…

Q: how long will it take an investment of $300 to triple, if the interest rate is 9.5% per year…

A:

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

A:

Q: Suppose income from an investment starts (at time 0) at $6000 a year and increases linearly and…

A: While calculating compound interest, the addition of interest to the principal sum of a loan or a…

Q: A survey estimates the current average cost of college to be $33,245per year.   ​(a) If the average…

A:

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

A:

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

A:

Q: How long would it take for a principal ofP to double if invested at 7% compounded continuously?

A: Given, for a principal of P to double if invested at 7% compounded continuously.

Q: Suppose that you have $2500 to invest at 4% compounded continuously.  The accumulated amount after…

A: Given investment amount $2500 and rate of interest r=4%=4100=0.04. Compounded continuously. The main…

Q: Determine the equivalent effective rate of a money compounded continuously at r=5%.

A:

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

A:

Q: A bank account earns 12% interest, compounded continuously, and has an initial balance of zero.…

A: Please check step 2 for the solution.!

Q: Suppose there is one pupil in a class of 60 who was infected by the Influenza B virus. Assuming none…

A: The logistic growth equation here is: P(t)=P0e0.7050t Where, P is the number of students inflected…

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: A continuous income stream has an annual rate of flow at time t given: f(t)=9000e^(0.12t)…

A:

Q: Savannah is going to invest $220 and leave it in an account for 12 years. Assuming the interest is…

A: We have, Savannah is going to invest $220 and leave it in an account for 12 years and at the end,…

Q: f you invest $10,400 at an interest rate of 2.5% compounded continuously, when will your investment…

A:

Q: Suppose that April has access to an investment that will pay 10% interest compounded…

A: Given, a situation, where April has access to an investment that will pay 10% interest compounded…

Q: Find the present value of a continuous income stream F(t) = 20 + 5t, where t is in years and F is in…

A:

Q: A money market fund has a continuous flow of money at a rate of f(x)=0.07x+100 for 10 years. Find…

A:

Q: Find the present value of a continuous income stream F(t) = 40 + 5t, where t is in years and F is in…

A:

Q: Suppose you invest $1200 at an annual interest rate of 2.3% compounded continuously. How much will…

A:

Q: Suppose that you want to have a $50,000 retirement fund after 40 years. How much will you need to…

A: Given query is to find the investment amount so that can give $50000 after 40 years.

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

A:

Q: A money market fund has a continuous flow of money at a rate of ​f(x)=1,900x−180x2 for 10 years.…

A:

Q: Find the amount that results from the given investment. $10 invested at 9% compounded continuously…

A:

Q: Suppose that a business provides a continuous income stream with an annual rate of flow at time t…

A:

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

A: Given Initial amountP=P0 Interest rater=6%=0.06 Time t=18 years Future valueA=70,000

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: 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: Suppose that P0 is invested in a savings account where interest is compounded continuously at 3.1%…

A:

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

A:

Q: Find the present value of a continuous income stream F(t) = 30 + 8t, where t is in years and F is in…

A: Given: A continuous income stream is: F(t)=30+8t Where t is in years and F is in thousand of dollars…

Q: Suppose that a population in a particular city is 46,581 in 2010. What is the population after 15…

A: The population growth is modelled using the equation: N(t)=N01+rt, where N0 is the initial…

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…

Q: How long will it take to double your money if it is invested at a fixed interest rate of 6%…

A:

Q: A money market fund has a continous flow of money at a rate of f(x)=0.07x+700 for 10 years. Find the…

A:

Q: How many years will it take $8,000 to grow to $12,900 if it is invested at 3.25% compounded​…

A:

Q: 2. At what rate of interest, compounded continuously will an investment double in six years? 3.…

A: (2) given that the principle amount will gets doubled in six years if the amount is compounded…

Q: An investor has $4000 to invest in either a bond that matures in 4 years or a business that will…

A:

Q: How much must one invest today in order to receive $20,000 after 5 years if interest is compounded…

A:

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.