This is also a recap of the module “Your Parents Will Move In With You”. For a discussion on how to arrive at this number, please see that module. If the class has done that module first, you can ask them for a quick description of how this was derived.
If not, you can have a short discussion about the size of this number. Does it seem big? Small? How often can you draw 130,000 from 1.5 million and have something left? This is not very many years of support, so what is assumed? We must assume this money is invested and drawing some rate of return.
In our example, the couple is using the account provided by the mother's employer.
Here comes the relevant algebra. If your students already did “Your Parents Will Move In With You” then this is basically a review. You might refer to their calculations in that module. The formula is the same, except instead of subtracting an annual amount here it is added. So a minus sign is replaced by a plus sign.
Otherwise you will have to go slowly. Have a look at the “Your Parents” module and instructor notes for ideas on how to fill in the gaps. An abbreviated version is in slides 10-13 of this module.
Alternatively, if you want to skip to the formula, you can go directly to slide 13.
This module provides a spreadsheet which your students may use to explore the decisions and calculations in this module. In particular, students can input an initial investment amount, yearly deposits, and an APR to find the balance after a fixed number of years.
At this point it would be good if the class were to experiment with different desired possible values of S25 and (1+i). For each of these a formula could be placed on the board.
Ask the students to write down the formula.
If your students did the “Your Parents” module, they might remember that 11% is much higher than the rate assumed for investments that continue during retirement. Why is this? You could have a good discussion here about return versus risk.
One standard piece of advice that people receive is to use riskier, higher yield investments while working, and lower yield but less risky investments after retirement. The word “aggressive” refers to the first kind of investing.
A measure of risk is “volatility”, which refers to the amount of variation in return that a particular investment yields.
Have them graph this line as A versus S0. What is the slope? Why is it negative? How much does S0 have to be in order for A to be zero? Does this make sense?
It is possible to double-check that answer by multiplying S0 by (1.11)25. Graphing the results of that calculation provides a visible reminder of exponential growth.
If you had the students repeat the calculation with various values for S0 and interest rate, then you can put up a collection of equations where each is a line. If your students are weak in algebra, it is particularly important to do this. You want students to see that a particular line represents a relationship between two quantities. But you also want them to think of a line as a mathematical object that satisfies certain criteria. In order to think that way, you have to be willing to consider multiple examples of lines at once. Here is a perfect opportunity to do that. You can then ask some questions such as:
Here is the explicit tie to the formula you usually see in algebra textbooks. It is good to make the link explicitly, even if you are not teaching this material as part of a “math” class.
If your students created a variety of formulas in slide 14, revisit them now to see a set of lines. You may wish to use the spreadsheet.
The line described in this slide is graphed on the spreadsheet
Students may use slider bars to vary three inputs: years to retirement, the ending balance, and the APR. These inputs determine the slope and y-intercept for a given scenario. The equation of the line appears on the graph.
Now we investigate various scenarios with the example in the module, but you can parallel this example with different interest rates.
When you get the answer to this particular question, you might ask the students what percent of their current income is represented by this amount. It is good to put this in perspective.
This answers the slide 18 question. Now have them do a few more. Plot the relationship and see that we obtain a line. Check the slope between two points and make sure it is what the formula indicates.
Do it again with this lower rate of interest. Manipulating algebraic expressions is a necessary skill for figuring this stuff out. Try a few more rates of interest and see what happens. The formulas generated at slide 14 would be good examples to explore here. Plot a few points for each choice of interest rate and see the different lines that result.
How does changing the interest rate affect the line? How does changing the desired amount available in 25 years affect the line
Exploring current interest rates, historical average rates of return, and realistic expectations will provide a basis for a rich classroom discussion.
Motivated students could change the 25 year period depending on the age of their parents.
So what does this say about “error bars”? What if our guess about average returns for the next 25 years is off by 2%? 5%? Have the students do some of these calculations.
The Social Security Administration claims that social security payments are intended as a supplement to retirement income or insurance against death of the wage earner in the family, and were never intended to foot the whole bill. Here is Roosevelt explaining this exact sentiment.
And here are some examples of people who currently benefit from social security.
In the next few slides we will see whether our couple's social security payments can offset the 2% reduction in growth of investments that may well be within the “error bars” for this estimate.
Have students do this calculation and see what a difference social security will make. Either you can have them redo the “Your Parents Will Move In” module to see how much the parents will need to have, or you can use the spreadsheet from that module.
Ultimately you want your students to do a complete analysis of their own or their parents' situation. This involves considering errors in interest rate estimation, errors in estimating how much is needed upon retirement, other sources of income such as social security. What else might we take into consideration? Have the students make suggestions.
Do students agree with any of the “experts” in the video? Why?
On what basis might the parents make this estimate? Students should mention debt, such as credit card, car and mortgage loans. Perhaps the parents assume they will not have the second two, nor much of the first. How about costs of commuting and so forth? But what about the BOAT?
Redo the calculation for this reduced lifestyle. Use the spreadsheet from this module.
Ask the students how many years it will be until they actually retire?
Students should be able to figure out that you should replace the 25 by 50. The conversation continues to be about the hypothetical parents as they leave college, who want to have a certain amount in the bank at 50 years time.
The spreadsheet also allows students to create a 50-year model.
What do you suppose the parents would have had as an income 25 years earlier if they now have $80,000? How would you calculate it based on a 2% decrease in value each year? They can do this by just taking (.98)25(80,000).
The question “are you saving that much now” is intended more as a behavioral prod. Actually, students can use their current salary, or estimated starting job salary, and the "Your Parents Will Move In" spreadsheet to figure out what they should be making 50 years from now using the same interest rates. Probably it will turn out that they should be saving more than this each year.
Indeed everything is never static, even for a single year. You can have a discussion about this and how you might introduce randomness into the calculation by having the interest rate vary each year in a random fashion.
If you were to incorporate a random element into the spreadsheet provided with this module, then of course you have to run the spreadsheet many times to see what it does on average. This is the basic idea behind a Monte Carlo simulation, a mathematical (or numerical) technique used in economics, business and finance. If you wish to try this, the "You Parents Will Move in" spreadsheet will serve as an example of how to proceed.
This goofy ending allows the discussion to return to the level of basic fear. What do we fear about getting old? Or our parents getting old? Mathematics allows us to get a handle on our fears, plan for the future, and take reasonable action now.
If you don't like the math, you can always get advice from other trusted sources such as this or this. Feel better now? Many counselors stand by, ready to profit from your fear and ignorance.