You are trying to decide how much to save for retirement. Assume you plan to sav

Question

You are trying to decide how much to save for retirement. Assume you plan to save $4,500 per year with the Est investment made one year from now You think you can earn 7.5% per year on your investments and you pian to retire in 28 years, immediately after making your last $4.500 investment a. How much will you have in your retirement account on the day you retire? b. 1f instead of investing $4,500 per year, you wanted to make one lump-sum investment today for your retirement that will result in the saine retirement saving, how much would that lump sum need to be? t. If you hope to live for 30 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 30th withdrawal (assume your savings will continue to earn 7.5% in retirement)? d. 1f instead, you decide to withdraw $79,000 per year in retirement (again with the Est withdrawal one year after retiring), how many years will it take until you exhaust your savings? (Use trial-and-error, a financial calculator: solve for N, or Excel: function NPER) e. Assuming the most you can afford to save is $900 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? (Use trial-and-error, a financial calculator: solve for the interest rate, or Excel: function RATE)

Explanation / Answer

Answer:

a. Amount in retirement account on the day of retirement =

Future value of the annuity regular = Annuity*{(1+interest rate)no of periods - 1}/(Interest rate)

                                                      = $4,500[{(1+0.075)28-1}/0.075] = $394,556.89

b. Let the lumpsum amount required to be invested today = X

   Now-   X*(1+0.075)28 = $394,556.89 => X = $394,556.89/7.576 = $52,079.84

c. Let Annual withdrawl from the retirement account is a annuity regualr = X

So the present value of annuity regular on retirement-

= Annuity*[{(1+interest rate)no of periods - 1}/{Interest rate*(1+interest rate)no of periods]

=> X[{1+0.075)30-1}/{0.075(1+0.075)30} = $394,556.89

=> X*(7.75/0.657)= $394,556.89 =>X = $394,556.89/11.81 = $33,408.71

d) Applying the Nper function in excel = NPER(7.5%,79000,394556.89,,0) = 4.4 years to exhaust the saving

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