Question

You are trying to decide how much to save for retirement. Assume you plan to save $8,000 per year with the first investment made one year from now. You think you can earn 8.5​% per year on your investments and you plan to retire in 39 ​years, immediately after making your last $8,000 investment. a. How much will you have in your retirement account on the day you​ retire? b.​ If, instead of investing $8,000 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 8.5​% in​ retirement)? d.​ If, instead, you decide to withdraw $435,000 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 $1,600 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)

Answer 1

a. We are given the following information

• PMT	$              8,000.00
  r	8.50%
  n	39
  T	1

• We need to solve the following equation to arrive at the required FV
• 
• 
• 
• So at the time of the retirement, the fund will have $2172774.46

b.​ We are given the following information

r	8.50%
n	39
frequency	1
FV	$      21,72,774.46

We need to solve the following equation to arrive at the required PV

So the lumpsum payment is 90210.04

c. We are given the following information

r	8.50%
n	24
frequency	1
PV	$      21,72,774.46

We need to solve the following equation to arrive at the required PMT

So we can withdraw 215038.96 annually for 24 years to completely exhaust the corpus

d.​ We are given the following information

r	8.50%
PMT	435000
frequency	1
PV	$      21,72,774.46

We need to solve the following equation to arrive at the required n

So the corpus will exhaust in 6.77 years

e.

We are given the following information

• PMT	$              1600
  r	8.50%
  n	39
  T	1

• We need to solve the following equation to arrive at the required r
• 
• 
• 
• So the rate of return needs to be 11.66% to accumulate the desired amount at the end of 39 years