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- You hire Thomas to work for you for five years, and you agree to put away enough money as a lump sum now to fund an annuity for him. At the end of those five years, he will retire and may begin drawing out $20,000 per year for five years, starting on the last day of each year (in this case, the end of year 6, from when this arrangement began, through year 10). How much must you invest today if your guaranteed interest rate is 3% compounded annually for all 10 years? (RESOURCE: Annuities) Note: Another two-stage present value problem, involving first finding a present value at a starting point (even though it occurs in our future!) that will generate a series of future payments and then calculating a single-amount present value today to achieve that future goal when payments (withdrawals) will begin. Please show how to solve for both steps, thank you!You plan to make a series of deposits in an individual retirement account. You will deposit $1,000 today, $2,000 in two years, and $2,000 in five years. If you withdraw $1,500 in three years and $1,000 in seven years, assuming no withdrawal penalties and all deposits and withdrawals are done at the start of specific year, how much will you have after eight years if the interest rate is 7 percent?You believe that you can set aside $1,200 each year for the next four years, starting immediately, in order to buy a small fishing boat for your retirement. Your friend Luis promises that he’ll pay you back $4,900 that he owes you three years from now, so you will add that to the payment you make at the start of year 4. Then, at the start of year 5, you will increase your payment to $1,400; in year 6, to $1,500; and in year 7, to $1,600. Every payment will be deposited in a fund bearing 4% interest compounded annually. How much will you have set aside for your boat at the end of the seventh year?
- A friend who owns a perpetuity that promises to pay $1,000 at the end of each year, forever, comes to you and offers to sell you all of the payments to be received after the 25th year for a price of $1,001. At an interest rate of 10%, should you pay the $1,000 today to receive payment numbers 26 and onwards? What does this suggest to you about the value of perpetual payments?Your uncle gives you $92,000 as a gift. Rather than give you a lump-sum, your uncle structures the gift as an annuity that pays $16,250 per year. You will receive the first payment one year later. If the annual interest rate is 12%, how many years does it take for you to receive all the payments for this gift?Bob purchases an annuity that will pay him $10,000 a year for the next 15 years starting a year from now. Assuming a 5% annual interest rate, what is the value of this annuity? Choose the closes. a) $150,000 b) $103,797 c) $124,622 d) $77,217
- You decide to open an individual retirement account (IRA) at your local bank that pays 8%/year compounded annually. At the end of each of the next 40 years, you will deposit $4,000 into the account. Three years after your last deposit, you will begin making annual withdrawals. What annual amount will you be able to withdraw if you want the withdrawals to last. Solve, a. 20 years ? b. 30 years? c. Forever?You wish to retire after 22 years; at which time you want to have accumulated enough money to receive an annuity of $68,000 a year for 25 years of retirement. During the period before retirement, you can earn 6 percent annually, while after retirement you can earn 4 percent on your money. What annual contribution to the retirement fund will allow you to receive the $68,000 annually?To supplement your retirement, you estimate that you need to accumulate $290,000 exactly 41 years from today. You plan to make equal, end-of-year deposits into an account paying 8% annual interest. a. How large must the annual deposits be to create the $290,000 fund by the end of 41 years? b. If you can afford to deposit only $800 per year into the account, how much will you have accumulated in 41 years?
- Suppose you want to provide for the college education of your son. He will begin college six years from now, and you wish to have $15,000 available for him at the beginning of each year in college. How much must be invested today at a 12 percent annual rate of return in order to provide the 4-year, $15,000 annuity for your son?To supplement your planned retirement in exactly 42 years, you estimate that you need to accumulate $220,000 by the end of 42 years from today. You plan to make equal annual end-of-year deposits into an account paying 8 percent annual interest.a. How large must the annual deposits be to create the $220,000 fund by the end of 42 years?b. If you can afford to deposit only $600 per year into the account, how much will you have accumulated by the end of the forty-second year?Amy Johnson wants to retire on $75,000 per year for her life expectancy of 20 years after she retires. She estimates that she will be able to earn an interest rate of 10.1%, compounded annually, throughout her lifetime. To reach her retirement goal, Amy will make annual contributions to her account for the next 30 years. One year after making her last deposit, she will receive her first retirement check. How large must her yearly contribution be? (Solve with Presents Values with Annuities or Loans and Amortization)
