You are trying to decide how much to save for retirement. Assume you plan to save $5000 per year with the first investment made one year from now. You think you can earn 10% per year on your investments and you plan to retire in 43 years, immediately after making you last $5000 investment. Required:
a. How much will you have in your retirement account on the day you retire?
b. If, instead of investing $3,000 per year, you wanted to make one lump-sum investment today for your retirement that will result in the same retirement saving, how mach would tat mp sum need to be?
c. If you hope to live for 20 years in retirement, how moch can you wihdraw every year in retirement (starting one year after retirement) so that you wil just exhaustyour savings with the 20th withdrawal (assume your savings will continue to earn 10% in retirement)?
d. If, instcad, you decide to withdraw $300,000 per year in retirement (again w the first withdrawal one year after retiring), how many years will isake until you exhaust your savings?

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

we need to find the future value of the annuity payments, we can use an annuity table to calculate this amount:

$5,000 x 592.4007 (FV of annuity, 10%, 43 years) = $2,962,003.50

b. If, instead of investing $3,000 per year, you wanted to make one lump-sum investment today for your retirement that will result in the same retirement saving, how mach would tat mp sum need to be?

we need to determine the present value of the future amount:

present value = future value / (1 + r)⁴³ = $2,962,003.50 / 1.1⁴³ = $49,170

c. If you hope to live for 20 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 20th withdrawal (assume your savings will continue to earn 10% in retirement)?

The maximum amount that you can withdraw per year starting one year after retirement would be $347,915.82 . This was calculated assuming that the investment account will continue to earn 10% annually.

d. If, instead, you decide to withdraw $300,000 per year in retirement (again w the first withdrawal one year after retiring), how many years will it take until you exhaust your savings?

if you retire "only" $300,000 per year, your savings should last at least 45 years.

Explanation:

a. $5,000 x 592.4007 (FV of annuity, 10%, 43 years) = $2,962,003.50

b. present value = future value / (1 + r)⁴³ = $2,962,003.50 / 1.1⁴³ = $49,170

c. $347,915.82 .  

d. The retirement is $300,000 per year, and last at least 45 years for saving

d. all of the above are true.