Assignment #1: Due April 1, 2009
Using some of the tools that we discussed in class, alter the IRA-accumulation program from class to accomplish the following:
1. We observed in class that our IRA will accumulate $141,521.58 when compounded for 30 years at %5 with IRA contributions of $2000.
Expand the class example of the IRA accumulation program to allow for the actual IRA contribution limits as follows:
For 2009, the annual contribution limit is $5000 for persons under 50 and $6000 for persons 50 and older. Beginning in 2010 and for each year thereafter this amount will increased annually based upon inflation. Assume that the IRS will allow an annual constant $250 increase. (See the discussion about IRA contributions from the about.com web site on the back of this handout.) Using the same interest-earned assumption (5% annually) that we did in the class example.
Now much money will you have accumulated when you reach 60 years old?
Expand the looping process to compute and display the IRA accumulation and usage for ages 30 to 90.
Assume that you make contributions from age 30 until age 60 based on the IRS guidelines with 5% interest earned annually on your balance and that you then will begin to withdraw $50,000 per year starting at age 60.
Assume that you will continue to earn 5% interest annually on any unused part of the IRA accumulation after the age of 60.
At what age will your IRA run out?
Adjust your program so that it reflects a higher interest rate (more aggressive investment) for ages 30 to 60 – let’s say 7.5 % annually -- and more a more conservative interest rate (less aggressive investment) after age 60 – say 3.5% .
At what age will your IRA run out now?
Just to make this realistic… expand the adjustment (question 3) above to account for inflation at 3.5% annually so that your annual withdrawal of $50,000 is based upon “Year-2009-dollars”. For example:
$50,000 Year-2009-dollars is worth $ 51,750 = $50,000 * 1.035 in 2010
$50,000 Year-2009-dollars is worth $ 53,561 = $50,000 * (1.035**2) in 2011
$50,000 Year-2009-dollars is worth $140,339 = $50,000 * (1.035**30) in 2039
$50,000 Year-2009-dollars is worth $393,905 = $50,000 * (1.035**60) in 2069
Now, at what age will your IRA really run out?
Recall that exponentiation is expressed as ** , e.g.: squaring is expressed as **2, cubing is expressed as **3 .
Turn in your SAS log and OUTPUT from #4 only, however note the “answers” to all of the questions (#1 - #4) on the first page. Your final printout should contain columns displaying (at the least) the calendar year, your age, IRA balance, IRA annual usage, and the annual interest rate.
Optional for the adventurous… (Biostatistics/Statistics majors and others?) Write a SAS program to accomplish the following: Choose 100 uniform random numbers and construct a suitable chi-square test to assess their uniformity. Note that critical values for the Chi-Square Distribution are available through the probchi(x,df) function. E.g. p-value for chi-square statistic of 10 with 20 degrees of freedom: probchi(10,20) = 0.03 . (David’s version of this program seeds the random number generator with the value 123 and uses 10 cells for assessing uniformity. It produces a (non-significant) p-value of 0.63308).