Funding your retirement Personal Finance Problem You plan to retire in exactly 2
ID: 2817866 • Letter: F
Question
Funding your retirement Personal Finance Problem You plan to retire in exactly 21 years. Your goal is to create a fund that will allow you to receive $21,000 at the end of each year for the 35 years between retirement and death a psychic told you that you would die exactly 35 years after you retire You know that you will be able to earn 11% per year during he 35-year retirement pen a. How large a fund will you need when you retire in 21 years to provide the 35-year, $21,000 ratiement annuity? b. How much will you need today as a single amount to provide the fund calculated in part a if you eam only 9% per year during the 21 years 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. No assume that you will eam 10% from now through the end of your retirement. You want to make 21 end-of-year deposits into your retirement account that will fund the 35-year stream of S21 000 annual annuity payments. How large do your annual deposits have to be? a. The amount of the fund you will need when you retire in 21 years to provide the 35-year, $21,000 retirement annuity is Round to the nearest cent.) b. The amount ou will need today as a single amount to provide the und calculated in part a f you earn only 9% per year during the 21 years preceding retirement is S Round to the nearest cent. 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? (Select from the drop-down menus.) 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 be needed in 21 years for the annuity and a d. Assuming that you will earn 10% from now through the end of your retirement, the amount of the fund will you need when you retire in 21 years is S Round to the nearest cent. In other words, a sum would amount would have to be put away today to accumulate the needed future sum.Explanation / Answer
a:N=35
Annuity = 21000
R=11%
Funds needed on retirement = PV of annuity = A*(1-1/(1+r)^n)/r
= 21000*(1-1/1.11^35)/0.11
=185960.04
B: N=21
R=9%
FV=185960.04
Funds needed today = PV= FV/(1+r)^n
= 185960.04/1.09^21
=30441.30
C:lower; lower;lower
If the rate post retirement increases, the amount will reduce since we will be discounting the annuity at a higher rate.
If the rate pre retirement increases, also the amount needed today will reduce due to a higher discounting rate.
D: N=21
R=10%
FV=185960.04
Amount of fund needed= 185960.04 (Since post retirement rate has not changed)
Annual deposits will be
FV= A*((1+r)^n-1)/r
A= 185960.04/ ((1.1^21-1)/0.1)
= $2905.51
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