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Mar 152013

A personal finance question that is asked on many accounting and financial professional exams is the Lifetime Savings Problem, in which one is asked how much one would have to set aside on a regular basis, beginning in one’s youth, in order to enjoy a retirement of a particular level. A typical example is:

Imagine that you planned to retire 30 years from now, and that you wanted to set up an account, into which you would make equal-sized payments each year during your working years, that would enable you buy an annuity that would pay you $25,000 at the end of each year for the 25 years immediately after you retired. Based on the expectation that your savings account should earn 9% per annum and that the retirement annuity should have a more conservative yield to maturity of 3% per annum, how much should you set aside each year until your planned retirement?”

This problem is in two parts: a) your retirement plan, and b) your savings plan to achieve that goal.

Savings Plan

Pay into Retirement Account

Retirement Plan

Draw from Retirement Account

A financial arrangement like the ones depicted above, in which payments—called coupon payments (c) for historical reasons—are made on a regular schedule for a specified period of time (t) is known as an annuity*. Here, the retirement account is an annuity that will pay you (perhaps, you will buy it from an insurance company or a large bank), and the savings account is an annuity that you will pay into (perhaps, a brokerage account or a statutory retirement account that you manage with the help of a financial professional).

To solve this puzzle you need to work backwards, first by deciding how much you would like to receive each year after you retire and for how many years; then by calculating the expected value—the price that you expect to pay, when the time comes—of an annuity that will provide for your retirement, which value becomes your savings goal; and finally by calculating how much money you should set aside each year between now and retirement, in order to achieve that goal.

Before you can know how much (c) to pay each year into a savings account that you open in your early years, you need to know how much you want to save. In other words, the price (APV for “annuity present value”) of the annuity that you plan to buy when you retire—the price that you expect to have to pay upon retirement—is exactly equal to the amount that you need save (AFV for “annuity future value”) during your working years. Tomorrow’s present value (i.e., price) is today’s future value.

Retirement Plan

If you imagined, for planning purposes, that you could live on $25,000 (c) per year after you retire, and that you wanted to plan for a 25-year (t) retirement—on the expectation that you’ll figure out a Plan B sometime during the next 55 years, in case you live beyond Year 26 after retirement—and that you expected your retirement account to earn 3% (r) per year, then you would need to save (APV):

This means that you need to have $435,329 on the day of your retirement, 30 years from now, so that you can buy the annuity that will pay $25,000 per year for 25 years.

Savings Plan

In order to save that amount (AFV), you plan to make equal annual payments (c) for the next 30 years (t), and you expect that you can earn an average of 9% per year (r) over that time.

If all goes according to plan, then, if you set aside $3,194 at the end of every year for the next 30 years and earn an average of 9% per year on your savings, then you should have $435,329 in three decades that you can use to buy an annuity that pays $25,000 per year for 25 years.

Invest accordingly.

Prof. Evans

note: For a detailed explanation of annuities, review my “Time Value of Money” video lecture. If you have difficulty viewing the videos try using VLC Media Player, “a free and open source cross-platform multimedia player and framework that plays most multimedia files as well as DVD, Audio CD, VCD, and various streaming protocols.” [return to main text]

Feb 052013

My expertise is in the field of Finance and Economics education, and not in the field of Criminology. I do not pretend to understand the underlying psychological and sociological causes of criminal behavior. However, I can identify a business opportunity when I see one.

Amy L. Solomon, a Senior Advisor to the Assistant Attorney General in the Office of Justice Programs at the US Department of Justice, wrote in the National Institute for Justice Journal (207, June 2012):

[N]early one-third of American adults have been arrested by age 23. This record will keep many people from obtaining employment, even if they have paid their dues, are qualified for the job and are unlikely to reoffend.

Granted, arrest does not always lead to conviction, and conviction does not always lead to incarceration, but the likelihood of getting called back for a second job interview drops by 50% for those whose background checks turn up an arrest. Those who have convictions or—Heaven help them—incarcerations on their records might as well forget ever being reintegrated fully into mainstream society, it seems.

Also, having an arrest record—just arrest, not even conviction or incarceration—can result in being denied entry into some countries, including US citizens who try to visit Canada.

Even more tragic, the effects are not uniform across the population.

One recent study estimates that 25 percent of African Americans born after 1990 will witness their father being sent to prison before their 14th birthday.

Imagine, for a moment, that you were born into a poor family living in a crime-infested part of town. Imagine, further, that you made some kind of mistake as a teenager—say, you were caught selling marijuana, possessing an unregistered firearm, or standing lookout for a local street gang—and you wound up going to jail. Mind, you never injured anyone; you were arrested for committing a victimless crime. You’re no angel, but you’re not a real danger to anyone, either.

While in jail, you would be distracted from advancing your education and developing the behavioral habits of mainstream society. Upon release, you would be behind your peers in school, perhaps you would feel angry and betrayed, and you would have developed a demeanor appropriate to surviving in jail and in a neighborhood populated by others with biographies and résumés similar to yours. Chances are that you would use illegal recreational drugs to take the edge off.

Now, you are barred from many jobs and from renting an apartment in all but the seediest neighborhoods, and you have no credit history. Nonetheless, you must eat and find shelter.

This is the day-to-day reality of a distressingly large proportion of the US population. For billions of humans outside the USA, the situation is only marginally better, regardless of criminal history.

What is a single individual to do about a problem this large, and—much more fundamentally—why would anyone who is not a Mother Teresa even want to bother?!?

A Proposal

As it turns out, someone has identified this niche and is doing something about it.

Defy Ventures [is] a yearlong, MBA-style program that [Catherine] Rohr created to teach former inmates how to start their own companies… Defy Ventures has raised more than $1.5 million in donations and pledges from VC firms, hedge funds, businesses, and private foundations.

We at Pecuniology.com propose to work with police departments, judges, parole boards, and charities, to provide Business education to those who have criminal histories and those at risk. This is based on the idea that, if one is a business operator, then one does not have to face the specter of drug tests and background checks.

As we demonstrate on this website, we are carving a niche for ourselves that involves the development of tutorials and practice utilities for students in Business disciplines.

This is a call to anyone who would like to incorporate our work into their programs, especially those who cater to the disenfranchised, worldwide. We have completed the proof-of-concept phase, and are using what already is available in a large government university. The next stage involves rounding out the Pecuniology.com offerings, so that they largely automate instruction, leaving facilitators on the ground free to focus on the specific and particular needs of face-to-face interactions.

Please share this with anyone who might be interested.

Invest accordingly.

Prof. Evans