20. am 30 years old but I am planning to retire at age 60. I want to plan my fin
ID: 1175713 • Letter: 2
Question
20. am 30 years old but I am planning to retire at age 60. I want to plan my finances for living to 95. If I make it to that day, then I will shoot myself so I do not need any money after that date. I want to die broke. I figure I need $6000 per month from age 60 on. I am not worried about inflation. At age 60, I plan to go live in the tropics on the beach and live on coconuts and fishing. I want to conclude my retirement savings at age 55 because all my spare money then will be going to finance my drug and alcohol business. Selling drugs and alcohol will finance my living expenses but will not allow me to contribute any more to my retirement plan because I expect to be ingesting all the profits. My questions (and yours) is how much do I have to save each month so I can quit contributing at age 55. I have nothing in the bank at this point. The expected return on my investments over the whole period is 6% per year.Explanation / Answer
The Present value of the monthly withdrawals of $6000 from the time of retirements can be calculated with the help of PV of an Annuity formula
PV = PMT * [1-(1+i) ^-n)]/i
Where,
Present value at the time of retirement (PV) =?
PMT = monthly payment =$6000
n = N = number of payments = 95 years -60 years = 35 years or 35 *12 = 420 months
i = I/Y = interest rate per year =6% or 6%/12 = 0.5% per month
Therefore,
PV = $6000 * [1- (1+0.5%) ^-420]/0.5%
= $1,052,281.36 (present value at the age of 60)
Now calculate the present value of the above amount at the age of 55
PV = $1,052,281.36/ (1+6%) ^5
= $786,325.84 (present value at the age of 55)
Now this amount will be future value of your current monthly savings for 25 years (55-30 = 25 years) at the rate of 6%/12 =0.5% monthly interest rate
For that we can use FV of an Annuity formula to calculate the monthly savings
FV = PMT *{(1+i) ^n?1} / i
Where,
Future value of monthly savings FV =$786,325.84
PMT = monthly savings =?
n = N = number of payments = 25 years * 12 = 300
i = I/Y = interest rate per year =6%, therefore monthly interest rate = 6%/12 = 0.5%
Therefore,
$786,325.84 = monthly savings *{(1+0.5%) ^300?1} / 0.5%
Monthly savings = $1,134.68 (assume that the saving is at the end of year)
Therefore you have to save $1,134.68 each month.
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