I recently retired, so deciding what my income is, deciding how quickly to drain my retirement account, has gained a new urgency. Unless the goal is to live off Medicaid, or its expected that the government will put us down once we reach our life expectancy, its important to have a plan. And since the future is even harder to predict than the past, its a plan that must be flexible, and can adjust with the economy. Its important to remember that accommodations made early in retirement will be smaller than the forced reductions made later.

I’m hoping to do this in three parts. First, look at some trial & error estimates based on subtracting annual amounts. Second, look at mortality tables and life expectancy. And third, try to come up with some algebraic expressions, or simple formulas to make periodic reassessment easier. Yes, this has been done by more knowledgeable people than me, but for my sanity, I want to know what goes into these estimates and understand why I should make sacrifices now.

For this article, I want to look at a baseline scenario, then include interest income, then investigate inflation, and finally both interest and inflation.

As a baseline we need to assume an initial account value, and a time interval it has to last. For these examples, I will assume a million dollars as the account value. This makes the expenditure rates easy to see as percentages. For a time interval, I’m choosing 40 years. I have heard advice that for financial planning purposes 100 years of age is a fair number to guess at. I sometimes wonder if I should plan for 105. While I don’t expect to reach 105 years, it may be prudent to plan for it. [I don’t expect to reach 100 either.] The old four score years is pretty likely insufficient, when life expectancy after reaching 65 is above 85. These two assumption lead to a constant expenditure rate of 1/40^{th} or 2.5% per year, i.e. $25000, or $25k, each year of the $1000k account. The data table uses an iteration of *A*_{i+1}*=A*_{i}*-x*, where *A* is the annual account balance, and *x* is the withdrawal amount, $25k in this case. When coupled with a pension and social security, this may be a helpful supplemental income.

Now lets look at the effect of interest on the balance. These days interest rates are non-existent to very low. I call them “sharia rates”, and my non-economist view is that they are low enough to discourage economic growth. But you can get 1% interest rates on long term Bank CD’s. Historically, stocks have averaged about 10% return over time. One could conceive of an investment strategy of 90% of the balance in “secure” investments on 10% in stock to yield about 2% return, or other investment mixes. I’ll look at two examples one with a conservative 1% return on the balance, and the other a close to an assumesd inflation rate of 3%. In this example, we deduct a constant amount each year, while increasing the balance each year by the interest rate, *A*_{i+1}*=(A*_{i}*-x)*(*1*+I) *where *I* is the annual interest rate.* *

You might guess that you could now withdraw 1/40^{th} + interest rate. While this initially tracks the annual balances of the baseline case, as the balance declines the the interest income does not keep up. For a 1% interest rate, a withdrawal rate of $30.5k lasts almost 40 years, while a 3% return, permits a withdrawal rate of $43k.

Now for the bad news, inflation. Present inflation rates appear to be 1% to 2%, however some of us think that including the necessary costs of food and fuel, while fluctuating a lot, increases the actual rate. The scary part is that there may be periods where inflation is much higher, hopefully they last only a few years, but present inflation rates are low, perhaps artificially low. I’ll assume an inflation rate of 3% for this example, but it will be important be aware of changing inflation rates, and accommodate higher rates by reducing withdrawals accordingly, not a desirable, but a necessary, accommodation. Assuming withdrawals increase 3% each year, with no interest income, means the starting withdrawal rate starts at only $13k, about half the baseline. The iteration equation for this is *A*_{i+1}*=A*_{i}*-(x*_{0}**((*1*+f)*^{i }*)), *where *x*_{0 }is the starting withdrawal rate, *f* is the inflation rate, and *i *is the year into the plan.

One other note, while I call this parameter “inflation” it is a planned increase withdrawal rate. If the real inflation rate is less than this, some of the difference can be left in the account. But if inflation is much more than is planned, for the sake of future needs, the withdrawals can’t be increased much.

Now lets look at the combination of interest and inflation. If the interest rate can match inflation, with both a 3%. An initial withdrawal rate of the baseline $25k lasts 40 years, with the final inflated withdrawal being nearly $80k. With a 1% return, the initial withdrawal can only be $16.3k. This is not a lot better than the no interest case. This exercise points out the importance of trying to match inflation rates or even exceed them with interest rates. And because the interest income dominates in the early years with higher account balances, it becomes difficult to match high inflation rate of later years. Strategies to deal with this risk may involve holding back a portion of the account, maybe base the initial withdraw on 90% of the account, or continue to save (maybe 10%) throughout the retirement years. And just for kicks lets assume we can get a slightly higher interest return than the inflation rate. For 4% interest, with a 3% inflation rate. A beginning withdrawal of $30k works. Note that this is 3% of the beginning balance, much less that the 4% spending rate I’ve heard bandies about only a few years ago. The iteration equation is now *A*_{i+1}*=(A*_{i}*-(x*_{0}**((*1*+f)*^{i }*)))*(*1*+I). *

While over an interval of 40 years it is foolish to ignore inflation, but it is prudent to accommodate only what is necessary. While I would like realize interest returns above inflation, it is prudent to only collect a fraction (½?) of the amount.

There is only one thing certain about these guesses at interest rates and inflation. That is, they are wrong. However, this method could be used to make reassessments every few years to accommodate economic changes.

Worksheet:

© 2014 David B Snyder