Suppose you deposit $9500 into an savings account earning 5% annual interest compounded continuously. To pay 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 initial condition. dA dt A(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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- 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 hereAssume 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. $10,488,912Suppose 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?)
- You are currently investing your money in a bank account which has a nominal annual rate of 7 percent, compounded monthly. How many years will it take for you to double your money? Identify the following variables to help solve problem: m Nper (or N) =n*m Rate (or I/Y)=i/m PV PMT FVSuppose you receive $100 at the end of each year for the next 3 years. a) if the interest rate is 8%, what is the present value of the cash flows? b) what is the future value in 3 years of the present value you compute in a? c) suppose you deposit the cash flows in a bank account that pays 8% interest in a year. What is the balance in the account at the end of each of the nest 3 years (after your deposit is made)? How does the final bank balance compare with your answer in b?Suppose you deposit $1,000 today (t = 0) in a bank account that pays an interest rate of 7% per year. If you keep the account for 5 years before you withdraw all the money, how much will you be able to withdraw after 5 years? Calculate using formula. Calculate using year-by-year approach. Find the present value of a security that will pay $2,500 in 4 years. The opportunity cost (interest rate that you could earn from alternative investments) is 5%. Calculate using the formula. Calculate using year-by-year discounting approach. Solve for the unknown in each of the following: Present value Years Interest rate Future value $50,000 12 ? $152,184 $21,400 30 ? $575,000 $16,500 ? 14% $238,830 $21,400 ? 9% $213,000 Suppose you enter into a monthly deposit scheme with Chase, where you have your salary account. The bank will deduct $25 from your salary account every month and the first payment (deduction) will be made…
- Use the tables in Appendix B to answer the following questions. A. If you would like to accumulate $2,500 over the next 4 years when the interest rate is 15%, how much do you need to deposit in the account? B. If you place $6,200 in a savings account, how much will you have at the end of 7 years with a 12% interest rate? C. You invest $8,000 per year for 10 years at 12% interest, how much will you have at the end of 10 years? D. You win the lottery and can either receive $750,000 as a lump sum or $50,000 per year for 20 years. Assuming you can earn 8% interest, which do you recommend and why?Use the tables in Appendix B to answer the following questions. A. If you would like to accumulate $4,200 over the next 6 years when the interest rate is 8%, how much do you need to deposit in the account? B. If you place $8,700 in a savings account, how much will you have at the end of 12 years with an interest rate of 8%? C. You invest $2,000 per year, at the end of the year, for 20 years at 10% interest. How much will you have at the end of 20 years? D. You win the lottery and can either receive $500,000 as a lump sum or $60,000 per year for 20 years. Assuming you can earn 3% interest, which do you recommend and why?Assume you just deposited $1,000 into a bank account. The current real interest rate is 2% and inflation is expected to be 6% over the next year. What nominal interest rate would you require from the bank over the next year? How much money will you have at the end of one year? If you are saving to buy a stereo that currently sells for $1,050, will you have enough to buy it?