Business, 29.07.2020 06:01 oliviakgobbell

You are trying to decide how much to save for retirement. Assume you plan to save $5,000 per year with the first investment made one year from now. ou think you can earn 11.0% per year on your investments and you plan to retire in 41 years, immediately after making your last $5,000 investment. a. How much will you have in your retirement account on the day you retire?
b. If, instead of investing $5,000 per year, you wanted to make one lump-sum investment today for your retirement that will result in the same retirement saving, how much would that lump sum need to be?
c. If you hope to live for 28 years in retirement, how much can you withdraw every year in retirement (starting one year after retirement) so that you will just exhaust your savings with the 28th withdrawal (assume your savings will continue to earn 11.0% in retirement)?
d. If, instead, you decide to withdraw $647,000 per year in retirement (again with the first withdrawal one year after retiring), how many years will it take until you exhaust your savings?
e. Assuming the most you can afford to save is $ 1 comma 000$1,000 per year, but you want to retire with
$1,000,000 in your investment account, how high of a return do you need to earn on your investments?

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Answer from: sofyan00404

a. How much will you have in your retirement account on the day you retire?

future value of the annuity = annual payment x (FV annuity factor, 11%, 40 periods) = $5,000 x 581.826 = $2,909,130

b. If, instead of investing $5,000 per year, you wanted to make one lump-sum investment today for your retirement that will result in the same retirement saving, how much would that lump sum need to be?

present value = future value / (1 + interest rate)ⁿ = $2,909,130 / 1.11⁴¹ = $40,320.04

c. If you hope to live for 28 years in retirement, how much can you withdraw every year in retirement (starting one year after retirement) so that you will just exhaust your savings with the 28th withdrawal (assume your savings will continue to earn 11.0% in retirement)?

payment = present value / annuity factor (PV annuity factor, 11%, 28 years) = $2,909,130 / 8.60162 = $338,207.22

d. If, instead, you decide to withdraw $647,000 per year in retirement (again with the first withdrawal one year after retiring), how many years will it take until you exhaust your savings?

We can first try to get an approximate answer. The annuity factor = $2,909,130 / $647,000 = 4.49633694. Now looking at an annuity table we can look at the closest amount for 11%. The answer is between 6 years (annuity factor 4.2305) and 7 years (annuity factor 4.7122). This means that in less than 7 years you will have no more money left.

e. Assuming the most you can afford to save is $ 1 comma 000$1,000 per year, but you want to retire with $1,000,000 in your investment account, how high of a return do you need to earn on your investments?

Again we must use the future value to determine the annuity factor. Annuity factor = $1,000,000 / $1,000 = 1,000. Using an annuity calculator to determine the closest rate (for 40 periods) = 12.9515% ≈ 12.95%

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You are trying to decide how much to save for retirement. Assume you plan to save $5,000 per year wi...