IRA Pay-Out

IRA’s (Individual Retirement Accounts) are good – for those who can afford them. At present you can put up to $2,000 a year into such an account, and reduce your taxable income by the amount of your deposit. You can not withdraw any money until the year in which you become 59 1/2 without suffering a penalty. Many banks have displayed ads telling how much you will have at retirement age, assuming a given rate of interest. Banks offer various options for the systematic rate of withdrawal of funds, but no such information has been advertised.

This program provides for a uniform rate of withdrawal. You must state the beginning amount (how much you have accumulated); the assumed rate of interest (a guess on anyone’s part); and the number of years of pay-out (must be equal or less than your life expectancy at retirement).

The process is called iteration. The amount of annual pay-out is first estimated by the variable, “c” and then the process is repeated until the balance left after the last payout is within one dollar of zero.

The first display shows the amount left after the last payout, alongside the annual payment. The second display shows the balance of funds for each year once the pay-out amount has been established.

  10 REM "IRA"
  15 REM - by Max Schoenfeld
  20 INPUT "How much money to start?  $ ";a
  30 INPUT "Expected interest rate? ";b
  40 INPUT "How many years to pay out? ";d
  50 PAUSE 50: PRINT "This table shows how much money remains in the account after ";d;" years, with the amount of annual withdrawal."
 100 PRINT : PRINT
 110 LET c=a/10
 120 DIM a(d+1)
 125 FOR x=2 TO d+1
 130 LET a(1)=a
 140 LET a(x)=a(x-1)*(b+1)-c
 150 NEXT x
 160 PRINT a(d+1);TAB 12;c
 200 LET c=c+a(d+1)/(2*d)
 205 IF a(d+1)<=1 AND a(d+1)>=-1 THEN GO TO 300
 210 GO TO 125
 305 PRINT : PRINT "Balance by year, after paying   out ";c-(a(d+1))/(2*d);" each year"
 307 FOR x=2 TO d+1
 310 PRINT (x-1);TAB 10;a(x)
 320 NEXT x
 330 PRINT : PRINT "Total pay-out is  $ ";d*(c-(a(d+1))/(2*d))
 340 STOP
 350 SAVE /"IRA PAYOUT"

Below is an example of how the program works. Start with $20,000 in the account. Assume an interest rate of .08. Plan for a 20 year pay-out.

This table shows how much money remains in the account after 20 years, along with the amount of annual withdrawal.

1695.2143   2000
-244.19408  2042.3804
35.175967   2036.2755
-5.067121   2037.1549
0.72983313  2037.0282

Balance by year after paying out 1037.0237 each year.
1         19562.972
2         19090.981
3         18581.232
4         18030.702
5         17436.13
6         16793.992
7         16100.483
8         15351.493
9         14542.585
10        13668.963
11        12725.452
12        11706.46
13        10605.949
14        9417.3963
15        8133.7598
16        6747.4323
17        5250.1987
18        3633.1863
19        1886.813
20        0.72983313

Total pay-out is  $ 40740.565

Line 350 was added by Don Lambert to save the program to a JLO disk. The text above is from the copy of this article on his Oliger disk, which matches the program in IRA Withdrawal. The example’s yearly payout is printed as 1037.0237; the table and the total correspond to about 2037.02 a year.