An endowment is to be invested with a continuous interest rate of 3 percent to yield a continuous stream of income 1000t dollars after t years. • For the endowment to produce the income stream for t from 0 to 20, how large an endowment is required? Explain. • For the endowment to produce the income stream forever, how large an endowment is required? Explain.

An endowment is to be invested with a continuous interest rate of 3 percent to yield a continuous stream of income 1000t dollars after t years. • For the endowment to produce the income stream for t from 0 to 20, how large an endowment is required? Explain. • For the endowment to produce the income stream forever, how large an endowment is required? Explain.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Unrestricted. Bacterial Growth A cenain colony of bacteria grows at a rate proportional to the…

A: The number of bacteria doubles every 12 hours. To determine: The time taken by the colony to grow to…

Q: In a central bank, continuous interest is given at a rate of 5% for each year, and every month,…

Q: A chemical reaction converts a certain chemical into another chemical, and the rate at which the…

Q: Use the formula for continuous compounding to compute the balance in the account after 1, 5, and 20…

A: Given that The deposit amount P=$ 16000Interest rate r=2.5%=2.5100=0.025 Time t=1 year…

Q: None

A: This problem can be solved using the concept of an infinite geometric series.Initial amount you…

Q: The number of cars sold weekly by a new automobile dealership grows according to a linear growth…

Q: When the price of a book is $125, a book store can expect to sell 600 books. If the price rises to…

Q: Assume that (x) = (20). Find Y and fy (r) in the life annuity pays according to the following table.…

A: Given information: It is given that (x) = (20).

Q: MATHEMATICS OF FINANCE QUESTION Units of RM1, are deposited at the beginning of each year for n…

Q: |Find the annual simple interest rate of a loan, where $900 is borrowed and where $954 is repaid at…

A: In the given question we have to find the simple interest rate of a lone whose borrowed and repaid…

Q: A chemical reaction converts a certain chemical into another chemical, and the rate at which the…

A: Let's find amount present initially.

Q: A person makes an initial deposit of $1000 (and no other deposits/withdrawals) into an account…

A: Let the number of full years completed be 'n'. ∴ The amount left after n years is given by…

Q: Year 2012 2013 2014 2015 2016 Deaths due to Lysol injections | 725 853 1046 1233 1453 (a) Find the…

A: The average rate of growth from 2013 to 2014 is given by: 1046-853=193 The average rate of growth…

Q: Find the time required for an investment of 7,000 dollars to grow to 14,000 dollars at an interest…

A: Given: Principal = $7000 Amount = $14000 Interest = 8% compounded monthly Formula used: A=P1+rnnt…

Q: Principal (P) Rate (r) Time (t) Interest (I) Maturity Value (F) (annually) |= Prt P1000 10% P100…

A: I = Prt , here we take rate (r) in decimal Maturity Value = Principal + Interest

Q: initial population =30,848 increasing at a rate of 3% what will the population be after 5 years

A: initial population = P0 = 30,848 Rate, r = 0.03 t = 5

Q: 6. Leticia's parents open a college savings account when she is born, depositing an initial amount…

A: initial amounta=$1000

Q: |The projected rate of increase in enrollment at Newhampton College is estimated by dE 5000(t +…

A: Given, The projected rate of increase the enrollment student at Newhampton college is estimated by…

Q: 1851,a person sold a house to a lady for $ 30.. If the lady had put the 36 info a bank acout paying…

A: The compound interest formula is , where A is the final amount, P is the principle amount, r is the…

Q: Practice #7 A population of x frogs increases at an annual rate of 22% at a local swamp. There were…

Q: ECONOMICS: 0il Demand The demand for oil in the United States is increasing by 3% per year. Assuming…

A: The demand for oil in the United States is increasing by 3% per year.Assuming that this rate…

Concept explainers

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.

Question

An endowment is to be invested with a continuous interest rate
of 3 percent to yield a continuous stream of income 1000t
dollars after t years.
• For the endowment to produce the income stream for t
from 0 to 20, how large an endowment is required?
Explain.
• For the endowment to produce the income stream forever,
how large an endowment is required?
Explain.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Find the time required for an investment of 5000 dollars to grow to 8000 dollars at an interest rate of 6.8 percent per year, compounded daily. _______________years.
Q4 Apopulation grows at the rate of (8%) per year. How long does it take for the population t become tripled a T~ 13 years 27 31 4 5 I~ 15 years T 14 Years. IN 12 Yearse T~ 11 years
PH [¹-(₁ + )¯] nt r 1+- n pay off the balance over three years. If there are no further purchases charged to the card, a. How much must you pay each month? b. How much total interest will you pay? Use PMT= to determine the regular payment amount, rounded to the nearest dollar. Your credit card has a balance of $4800 and an annual interest rate of 13%. You decide to a. The monthly payments are approximately $ (Do not round until the final answer. Then round to the nearest dollar as needed.) b. The total interest paid over 3 years is approximately $. (Round to the nearest dollar as needed.)
2. Lijah opened an account at Advantis Credit Union. The balance of her account after x years is represented by the function b(x) = 500(1.05)*. What annual interest rate is Lijah earning? а. b. After how many years did it take for Lijah's balance to double? Show all of your work.
A certificate of deposit is worth P (1+r)t dollars after t years, where r is the annual interest rate expressed as a decimal, and P is the amount initially deposited. Which investment will be worth more? Investment A, in which P =$7300, r=4%, and t=5 years. Or investment B, in which P= $6300, r=6%, and t= 7years. Round to two decimal places. The value of certificate A will be what? And the value for investment B will be what? And which is worth more, A or B?
A new car costs $27, 000 depreciates to 80% of its value in 2 years. Round all answers to 2 decimal places, where necessary. a. Assume that the depreciation is linear. What is the linear function that models the value of this car t years after purchase? f(t) = Preview b. Assume that the value of the car is given by an exponential function Aekt, where A is the initial price of the car. Find the value of the constant k. Answer exactly. k = Preview c. For the linear model used in part (a), find the value of the car 6 years after the purchase, then do the same for the exponential model used in part (b). Round your answer to 2 decimal places. Linear after 6 years: $ Exponential after 6 years: $
Advanced Math will upvote