partial credit, P5-24 (similar to)

Funding your retirementPersonal Finance ProblemYou plan to retire in exactly 24years. Your goal is to create a fund that will allow you to receive $20, 000at the end of each year for the 25years between retirement and death (a psychic told you that you would die exactly 25years after you retire). You know that you will be able to earn 9% per year during the 25-year retirement period.

a.How large a fund will you need when you retire in 24years to provide the 25-year, $20, 000

retirement annuity?

b.How much will you need today as a single amount to provide the fund calculated in part a if you earn only 7%

per year during the 24years preceding retirement?

c.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.

d.Now assume that you will earn 8% from now through the end of your retirement. You want to make 24, end-of-year deposits into your retirement account that will fund the 25-year stream of $20, 000annual annuity payments. How large do your annual deposits have to be?

a. The amount of the fund you will need when you retire in 24years to provide the 25-year, $20,000 retirement annuity is

$194132.24

b.The amount you will need today as a single amount to provide the fund calculated in part a if you earn only 7% per year during the 24years preceding retirement is $38272.51

c.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 andb?

In the calculation of present values, you should notice that the higher the interest rate, the lower the present value. Therefore, in part a and b both values would be:lower, higher or equal

. In other words, a smaller, higher, or equal. sum would be needed in 24 years for the annuity and a , higher or equal or smaller amount would have to be put away today to accumulate the needed future sum.