Question 350135: Suppose you would like to be paid $20,000 per year during your retirement, which starts in 20 years. Assuming the $20,000 is an annual perpetuity and the discount rate is an effective 4% per year, how much should you save per year for the next 20 years so that you can achieve your retirement goal?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! If you want to be paid $20,000 per year for the rest of your life without the balance of the fund going down, and assuming that the interest rate at which the account will increase each year is 4%, and you expect to start withdrawing the money immediately in year 20, then the amount of money that needs to be in the fund is equal to $520,000.
That's equivalent to $20,000 / .04 = $500,000 plus $20,000 to be withdrawn immediately to make a total of $520,000 required to be in the account in year 20.
If you have to figure in taxes, then the amount taken out each year will have to pay the going tax rate, and you will have to have more than $500,000 in the account to start with in order to cover the withdrawal plus taxes on the withdrawal.
We'll forget about taxes for sake of simplicity.
You will need to have $520,000 in the account 20 years from now.
If this is year 0, then year 20 is an additional 20 years from now.
If the investment rate is 4%, then you would need to invest $237,321.212 today in order to have $520,000 in the account in year 20.
The formula to use to calculate the present value of the future amount of $520,000 is shown below:
PRESENT VALUE OF A FUTURE AMOUNT
PV = Present Value
FA = future amount
i = Interest Rate per Time Period
n = Number of Time Periods
I used this formula to duplicate the result that I obtained through the use of a financial calculator.
You should be able to duplicate the result also.
i = .04
n = 20
FA = $520,000
PV is calculated to be
On a yearly cash flow analysis, this is what it would look like:
ACCOUNT ACCOUNT
YEAR BALANCE WITHDRAWAL
0 $237,321.21 $0.00
1 $246,814.06 $0.00
2 $256,686.62 $0.00
3 $266,954.09 $0.00
4 $277,632.25 $0.00
5 $288,737.54 $0.00
6 $300,287.04 $0.00
7 $312,298.52 $0.00
8 $324,790.47 $0.00
9 $337,782.08 $0.00
10 $351,293.37 $0.00
11 $365,345.10 $0.00
12 $379,958.91 $0.00
13 $395,157.26 $0.00
14 $410,963.55 $0.00
15 $427,402.10 $0.00
16 $444,498.18 $0.00
17 $462,278.11 $0.00
18 $480,769.23 $0.00
19 $500,000.00 $0.00
20 $520,000.00 $20,000.00
21 $520,000.00 $20,000.00
22 $520,000.00 $20,000.00
23 $520,000.00 $20,000.00
24 $520,000.00 $20,000.00
25 $520,000.00 $20,000.00
The money is invested in year 0 and grows at 4% per year until year 20 at which point 20,000 is withdrawn each year keeping the balance at a steady $520,000.
I went to year 25 to show you that the account balance remains the same, despite the $20,000 withdrawal each year.
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