P5-24 only please

Funding your retirement You plan to retire in exactly 20 years. Your goal is to create a fund that will allow you to receive $20,000 at the end of each year for the 30 years between retirement and death (a psychic told you that you would die exactly 30 years after you retire). You know that you will be able to earn 11% per year during the 30-year retirement period. How large a fund will you need when you retire in 20 years to provide the 30-year, $20,000 retirement annuity? How much will you need today as a single amount to provide the fund calculated in part a if you earn only 9% per year during the 20 years preceding retirement? What effect would an increase in the rate you can earn both during and prior to retirement have on the values found in parts a and b? Explain. Now assume that you will earn 10% from now through the end of your retirement. You want to make 20 end-of-year deposits into your retirement account that will fund the 30-year stream of $20,000 annual annuity payments. How large do your annual deposits have to be? Personal Finance Problem Value of an annuity versus a single amount Assume that you just won the state lottery. Your prize can be taken cither in the form of $40,000 at the end of each of the next 25 years (that is. $1,000,000 over 25 years) or as a single amount of $500,000 paid immediately. If you expect to be able to earn 5% annually on your investments over the next 25 years, ignoring taxes and other considerations, Which alternative should you take? Why? Would your decision in part a change if you could earn rather than 5% on your investments over the next 25 years? Why? On a strictly economic basis, at approximately What earnings rate would you be indifferent between the two plans.? Perpetuities Consider the data in the following table