The following initial value problem model the payoff of a loan. In each case, solve the initial value problem, for t ≥ 0, graph the solution, and determine the first month in which the loan balance is zero. B'(t) = 0.004B - 800, B(0) = 40,000

Q: If P dollars are invested for t years at a simple interest rate​ r, the future value of the…

A: follow next step

Q: Investment A offers a 9% return compounded semiannually, and investment B offers a 8.81% return…

A: Given that, Investment A offers a 9% return compounded semiannually Investment B offers a 9.81%…

Q: You invest $20,000 in the bank with a 5% annual interest rate, compounded continuously and you…

A: Let the amount of money at anytime be p(t)=dpdt=Pi-k where k is the withdrawal amount rate…

Q: Two investments, A and B, produce a continuous income stream of 3%, compounded continuously. The…

A: A and B continuously produces income stream 3% compounded annually  ft=3000e0.04tgt=5000 we have to…

Q: Question 20 After montls of negotiations, Jalm's anal salary wis increased by 635 t R330 000.…

A:

Q: Fund A) has force of interest St = .024t (where t is in years) while fund B) earns a nominal…

A:

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: You are contemplating driving an underground airway at a cost of $1,750,000. The airway will be used…

A: I am assuming that the loan is paid in the form of EMI. Thus, monthly amount paid over 7 years is:

Q: The following initial value problem models the payoff of a loan. Solve the initial value problem for…

A:

Q: Jay wants to invest $5,000 in an account with an interest rate of 8.5% that is compounded MONTHLY.…

A:

Q: In return for 1000 in 5 years, Mary agrees to pay 200 now, X in 3 years and 1 2X in 10 years. Find X…

A: To calculate x as shown below:

Q: 4) The formula for the depreciation of a car is A = P (1-", where A is the depreciated value (final…

A:

Q: ipounded instantaneous interest rate curve is given by 6. Assume that the ri(t) = 0.02 + 0.05 In(1…

A: Given :The Continuously compounded zero rate curveri (t) = 0.02 + 0.05 ln(1+0.2t)

Q: Land bought for speculation is increasing in value according to the formula V – 1000e Ve The…

A:

Q: A 120. MW coal plant wants to add a SOx emissions control system to reduce its emissions. The…

A: Consider the given information:

Q: A 10 year continuous annuity pays at a rate of t at time t. If v^t = .94t, calculate the accumulated…

A:

Q: Determine the deposit amount X at time 2 that will provide for a payment of $9000 at time 6 given…

A: Definition of accumulation function a(t) describes the accumulated value at time t of initial…

Q: Fund A of $ 5,000 grows with an instant interest rate of St =1/(12-t) for 0 <t <12. B fund of $…

A: Given, δt=112-t for 0&lt;t&lt;12 In case of A: Principal(P)=$5000 Time=11 Then the interest rate (r)…

Q: If $P is invested for n years at 12% compounded continuously, the future value that results after n…

A: deandn=a.ean

Q: A colony of rats is transplanted into an island environment by stowing away on a cargoship. The…

A: Given that  A colony of rats is transplanted into an island environment by stowing away on a…

Q: If the principal P is invented at an interest rate r compounded anually, the amount A after t years…

A: Given P = 10000A = 20000r = 15%

Q: - Find the time required for an initial investment of $2000 to reach $7500 if the interest is…

A:

Q: Find the future value P of each amount P, invested for time pe- riod t at interest rate k,…

A:

Q: Assume that you are 30 years old today (t=0) and that you plan to retire at age of 65 (t=35). Your…

A: Assume that you are 30 years old today (t=0) and that you plan to retire at age of 65 (t=35). Your…

Q: An investor is presented with an investment proposal which produces a continuous income stream of…

A: let's find future value of the investment and interest earned.

Q: The following initial value problem model the payoff of a loan. In the case, solve the initial value…

A: given: B'(t)=0.01B-750 B(0)=45000 the given differential equation is:…

Q: a) Find the present value of $34000 payable at time t = 7 relative to timet = 3. Answer = $ %3D b)…

A: a Let present amount =xintrest at time t=7 relative to time t=3x0.24+0.015×2+x0.37-0.021×2now total…

Q: The future value of a simple interest investment is given by S=P(1+RT) What principal P must be…

A:

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: The following initial value problem model the payoff of a loan. In each case, solve the initial…

A: Consider the initial value problem that represents the payoff of a loan B'(t)=0.0075B-1500,…

Q: The formula for the amount A in a savings account compounded n times per year for t years at an…

A: You just need to find the limit of the given expression when 'n' is tending to infinity.

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: Find the accumulated future value of the continuous income stream at rate R(t), for the given time…

A:

Q: With an annual rate of inflation of 3% over the next 10 years, the approximate cost C of goods or…

A: Given that: Cost of good, C(t)=P(1.03)t Initial cost of oil = $24.97

Q: A businessman intends to buy a bungalow and he is going to get a home loan. He can afford to make…

A: Part(a): Let yt be the loan balance after time t. Also businessman makes the payment of RM 400000…

Q: The annual net income of a company for the period 2007-2011 could be approximated by P(t) = 1.6t2. -…

A: The annual net income is defined as pt=1.6t2-11t+43 billion dollars where t is the years since the…

Q: The annual net sales (revenue) earned by Nintendo in the fiscal years 2000 – 2014, can be…

A: If the fiscal year starts from 2006 to the start of fiscal year 2014 of Nintendo . t is the time in…

Q: If a principal P is invested at an annual rate r compounded n times a year, then the amount A at nt…

A:

Q: 2. In the formula A(1) = Pe" for continuously compound inter- est, the letters P, r, and t stand for…

A: Given,

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

A:

Q: A young person with no initial capital invests k dollars per year at an annual rate of return r.…

A: a) Set up the initial value problem. Let S(t) be sum of money at time t measured in years Initial…

Q: A loan of R20 000 is to be amortised by means of five regular equal monthly payments of R5000…

A: Given: P=20000, I=5000, t= 612 We have I=Prt1005000=20000× 612×r100100r-5000=0 Consider the…

Q: The following initial value problem models the payoff of a loan. Solve the initial value problem for…

A:

Q: Find the accumulated future value of the continuous income stream at rate R(t), for the given time…

A:

Q: 3. The rate of growth of an investment is proportional to the amount of the investment at any time…

A:

Q: For a 3-year term insurance at age x with death benefit of 1,000 (with death benefit payable at end…

A: Given, px=0.97i=6%x=153Number of premiem is 56 Present Value of Death Benefits: Death Benefits…

Q: In the year 2000, the population of a certain country was 285 million with an estimated growth rate…

A: Initial population, P0 = 285 million Growth rate, r = 0.5% = 0.005 Use the exponential growth…

Q: 2) y = -2 (5)* Initial Value: Constant Ratio: Asymptote:

A:

Q: Suppose that the spot price of copper is $3.25 per pound, the continuously compounded lease rate for…

A: Given: Suppose that the spot price of copper is $3.25 per pound, the continuously compounded lease…

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.