# Fund Drawdown Simulation

This Demonstration lets you estimate the value of a pool of money (the fund) that increases in value due to an investment return on the fund (at rates between 0 and 10% per year) and decreases in value due to an annual withdrawal. An example would be to estimate how the value of a college fund changes over the four years that tuition and living expenses are withdrawn, while the balance of the fund continues to earn interest. Similarly, the value of a retirement nest egg can be estimated under a situation where the retiree makes annual withdrawals.

### DETAILS

A change in the "annual withdrawal increase" applies the selected fractional increase to the value set by the "initial annual withdrawal (\$000s)". For example, if the initial annual withdrawal is set at \$1000 and the annual withdrawal increase is set at 0.05 (to counter the effects of inflation, say), then the annual withdrawal for the second year will be \$1000 x 1.05 = \$1050. The annual withdrawal for the third year will be \$1050 x 1.05 = \$1102.50 and so on.
Here is an equation:
,
where is the annual return as a fractional value, is the annual fractional increase in the withdrawal, and is the chosen initial annual withdrawal rate.
This Demonstration solves the above differential equation over a settable range of years, up to 30 years. When the constant annual withdrawal exceeds the investment return, the value of the fund declines over time. In this situation, the "value (\$K)" column of the table may turn negative. In this case, the fund has been exhausted and the additional rows and columns of the table are not meaningful.

### PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Curriculum Standards

US Common Core State Standards, Mathematics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.