Suppose you deposit $9500 into an savings account earning 5% annual interest compounded continuously. Topay for all your music downloads, each year you withdraw $1000 in a continuous way.Let A(t) represent the amount of money in your savings account t years after your initial deposit.(A) Write the DE model for the time rate of change of money in the account. Also state the initialcondition.dAdtA(0)(B) Solve the IVP to find the amount of money in the account as a function of time.A(t)=(C) When will your money run out?t =years

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Answered: Suppose you deposit $9500 into an…

Principles of Accounting Volume 2

19th Edition

ISBN:9781947172609

Author:OpenStax

Publisher:OpenStax

Chapter11: Capital Budgeting Decisions

Section: Chapter Questions

Problem 3PA: Use the tables in Appendix B to answer the following questions. A. If you would like to accumulate...

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You initially invest $400 in a savings account that pays a yearly interest rate of 3%. (a) Write a formula for an exponential function giving the balance in your account as a function of the time since your initial investment. (Let B be the account balance in dollars and t be the number of years since the initial investment.) 8(t)= dollars (b) What monthly interest rate best represents this account? Round your answer to three decimal places. % (c) Calculate the decade growth factor. (Round your answer to two decimal places.) (d) Use the formula you found in part (a) to determine how long it will take for the account to reach $536. (Round your answer to the nearest whole number.) yr Explain how this is consistent with your answer to part (c), At the end of one decade, there will be $ where the account reaches $536 at the end of This --Select-- o the answer found above years,
One can solve for payments (PMT), periods (N), and interest rates (1) for annuities. The easiest way to solve for these variables is with a financial calculator or a spreadsheet. Quantitative Problem 1: You plan to deposit $2,100 per year for 4 years into a money market account with an annual return of 3%. You plan to make your first deposit one year from today. a. What amount will be in your account at the end of 4 years? Do not round intermediate calculations. Round your answer to the nearest cent. $ b. Assume that your deposits will begin today. What amount will be in your account after 4 years? Do not round intermediate calculations. Round your answer to the nearest cent. $ Quantitative Problem 2: You and your wife are making plans for retirement. You plan on living 25 years after you retire and would like to have $95,000 annually on which to live. Your first withdrawal will be made one year after you retire and you anticipate that your retirement account will earn 12% annually. a.…
You open a savings account with $1,000. At the end of each year you earn 3% interest on your savings and then you deposit $1,000 into the account. Let An be the amount in the account after n years. 1. Explain why A₁ = 2,030. 2. Calculate A2 and A3. Round to the nearest penny if necessary. 3. Write a recurrence relation for An+1 in terms of An. What is the first term A₁?
Suppose you deposit $10 every week into an account that earns 4% interest compounded weekly. How much money (to the nearest cent) will you have in the account after 5 years? Summarize the information provided, stating the interest rate in a decimal form. d = r = N = k = Solve the problem and give your answer here
Assume that you have $10,000,000 in your bank account. You wish to withdraw $400,000 per year, at the end of each year, for the next 5 years, after which you wish to have $11,000,000 in the bank. What is the balance in your account after the 2nd year (after the withdrawal)? Hint: you will need first to solve for rate in Excel given all other parameters. Watch signs. Select one: a. $10,366,644 b. $10,600,000 c. $9,600,000 d. $10,488,912
Suppose you deposit m dollars the beginning of every month in a savings account that earns a monthly interest rate of r. For an initial investment of m dollars, the amount of money in your account at the beginning of the second month is the sum of your second deposit and your initial deposit plus interest. Denote by An the amount of money in your account in the nth month. 1. Explain why A₁ = m dollars. 2. Explain why A₂ = m+m(1+r) dollars. 3. Write down explicit expressions for A3 and A4. This is the crucial step. 4. Explain why An = m+m(1 + r) + m(1 + r)² + ... +m(1 + r)"−¹ dollars. 5. Use the formula for a geometric sum to show that An = m (1 + r)” − 1 r dollars. 6. If your account has a monthly interest rate r = 0.002 and you deposit $200 monthly for 5 years, how much money will you have in your account after the 5 years? (Hint: How many months?)
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In this project, you will use a graphing calculator to compare savings plans. For instance, suppose you are depositing $1000 in a savings account and are given the following options: 4 • 6.2% annual interest rate, compounded annually 6.1% annual interest rate, compounded quarterly 6.0% annual interest rate, compounded continuously •
Solve the following problem with a full solution without using excel.
Please answer all subparts with explanation. I will really upvote. Thanks
You were saving your money in an account that requires interest continuou at a rate of 6.25%. You invested $12,000. part A: identify the values for the variables, in write an equation that can be used to find the amount of money and they count after a certain number of years, T. part B: approximately how much money will be in the account after two years, show your work. part C:
The balance of an interest-bearing account can be modeled by an exponential equation. For example, consider an initial deposit of $10000 at an annual interest rate of 5%. The interest earned each year is deposited into the account at the end of the year. A. Assuming that no withdrawals or deposits are made, write an equation that models the account balance after x years. Your answer B. What is the account balance at the end of the 7 years? Your answer C. Create a graph that shows the increase in the account balance over the next 15 years, including your initial deposit. Your answer D. Using the graph, estimate how many years it will take for the initial deposit to double. Your answer E. If you deposited $5000O in an account of this type, what would the account balance be when you are 50 years old assuming that you are 20 years of age right now? Your answer OCT 16

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