Question

You are trying to decide how much to save for retirement. Assume you plan to save$4,000 per year with the first investment made one year from now. You think you can earn 6.0​%per year on your investments and you plan to retire in 39 ​years, immediately after making your last $4,000 investment.

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

b.​ If, instead of investing $4,000 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 24 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 24th withdrawal​ (assume your savings will continue to earn 6.0​% in​ retirement)?

d.​ If, instead, you decide to withdraw $116,000 per year in retirement​ (again with the first withdrawal one year after​ retiring), how many years will it take until you exhaust your​ savings? (Use​ trial-and-error, a financial​ calculator: solve for​ "N", or​ Excel: function​ NPER)

e. Assuming the most you can afford to save is $800 per​ year, but you want to retire with $1,000,000in your investment​ account, how high of a return do you need to earn on your​ investments? (Use trail-and-error, a financial calculator: solve for the interest rate, or Excel: function RATE)

Answer 1

a.Information provided:

Annual saving= $4,000

Time= 39 years

Interest rate= 6%

The question is solved by calculating the future value of ordinary annuity.

Enter the below in a financial calculator to compute the future value of ordinary annuity:

PMT= -4,000

N= 39

I/Y= 6

Press the CPT key and FV to compute the future value of ordinary annuity.

The value obtained is 580,233.83.

Therefore, the amount in the account on the day I retire will be is $580,233.83.

b.Information provided:

Future value= $580,233.83.

Time= 39 years

Interest rate= 6%

The question is calculated by computing the present value.

Enter the below in a financial calculator to compute the present value:

FV= 580,233.83.

I/Y= 6

N= 39

Press the CPT key and PV to compute the present value.

The value obtained is 59,796.30.   

Therefore, the lumpsum needed to have the same retirement saving is $59,796.30.

c.Information provided:

Present value= $580,233.83

Time= 24 years

Interest rate= 6%

The annual withdrawal is calculated by entering the below in a financial calculator:

PV= -580,233.83.

N= 24

I/Y= 6

Press the CPT key and PMT to compute the amount of annual withdrawal.

The value obtained is 46,232.45.

Therefore, the amount of annual withdrawal is $46,232.45.

d.Information provided:

Present value= $580,233.83

Interest rate= 6%

Annual withdrawal= $116,000

The question is solved by calculating the time taken exhaust my savings.

Enter the below in a financial calculator to compute the time taken exhaust my savings:

PV= -580,233.83

PMT= 116,000

I/Y= 6

Press the CPT key and N to compute the time taken exhaust my savings.

The value obtained is 6.1242.

Therefore, it will take 6.12 years to exhaust my savings.

In case of any query, kindly comment on the solution.