Time is Money or Time Earns Money

Compound interest is the most powerful force in the universe.
- Albert Einstein


In Forbes recently, Robert Lenzner reports Financial Illiteracy Widespread in America.

A huge swathe of the American population are illiterate with respect to their finances and lack basic skills in dealing with numbers, a highly respected economic think-tank, the National Bureau of Economic Research in Cambridge, Mass. concluded in a recent working paper by Annamaria Lusardi. The National Bureau of Economic Research has a close relationship with Harvard University, and many leading Harvard economists like Martin Feldstein are active members and leaders of the research there.

“Financial illiteracy and lack of numeracy are not only widespread in the population, but are particularly severe in certain demographic groups,” the paper concludes. The most vulnerable groups in the population are the elderly, women and those with “the lowest educational attainment.”

The study underscores the difficulty these subgroups experience in any kind of financial decision-making. This is particularly dangerous when facing the capacity to do calculations, debt management and asset building. This worrying reality faces new challenges as the federal government copes with the need to control the cost of Social Security, and Medicare– both essential federal programs essential for survival.

Clearly, the nation must revitalize its educational programs in basic mathematics and apply this knowledge to the job of managing household wealth and expanding it– a very tall order.

These days a lot of education talk centers around teaching-to-the-test, which I interpret as teachers focusing on having students answer the questions found on standardized tests. I must admit I have no idea what is tested, but as I now have small children, I often think about what skills should be taught in school.

Due to my education in engineering and my fondness of economics and finance, it will come as no surprise that I think math/numeracy is very important.  Likewise grammar and writing are very important too because everyone need to be able to effectively communicate using the written word.  It may surprise you that I spent more time with tutors on these subjects than any other in college.  Still I get it that every person has strengths and weaknesses.

Yet it is unacceptable that schools are failing to educate students in applying mathematical principles to managing one's finances.  As these skills are used daily no matter what your profession, it is part of the foundation of skills that lead to a successful life.  And if the foundation of anything is questionable, then so is everything that is built on that foundation.

At the end of Emergency Funds and Austerity are not Only for Greece, I began a short section in 14minuteinvestor called Learning from the Ground Up.  The primary purpose of this section is to educate readers on financially essential topics that will be used in their lifetime.

Learning from the Ground Up

Today's essential topic is the time value of money.  According to Wikipedia:

The time value of money is the value of money figuring in a given amount of interest earned over a given amount of time.

The reason time value of money is important to you is because it's the central concept in finance theory.  You can use it, or one of it's derivations, to calculate many useful answers, such as:

• Simple Interest - how much money is earned from your original investment.
• Compound Interest - how much does your money grow when your interest also earns interest.
• Present value or future value of an annuity.
• Present value or future value of a perpetuity.
• Present value (balance) of a mortgage.

Thus the benefit of applying time value of money is you can wisely choose between two or more investment decisions. 

Before I begin though, I make a few assumptions about my readers capabilities.  Readers need to be able to:

1. Calculate using basic mathematics such as addition, subtraction, multiplication, division, and exponentiation.
2. Perform calculations while following proper order of operations.
3. Perform calculations using a spreadsheet in order to save time and add complexity.

Using the following equation, the future value of money can be calculated if you know how much you invest, the interest rate, and how often it compounds.

• FV = future value of your investment
• PV = present value of your investment
• n = number of years invested
• r = interest rate
• t = number of times interest compounds during a year

Let's start simple using the following example.  I have $1000 and I want to know how much I will have at the end of 1 year if it compounds annually at a 5% interest rate.

• PV = $1000, n = 1 year, t = 1 since it's compounded annually, r = 5% or 0.05

• FV = $1050

Let's add an infinitesimal amount of complexity.  I want to know how much I will have at the end of 5 years.

• PV = $1000, n = 5 year, t = 1 since it's compounded annually, r = 5% or 0.05

• FV = $1276.28

Let's add a little more complexity.  I want to know how much I will have at the end of 5 years if interest compounds daily.

• PV = $1000, n = 5 year, t = 365 since it's compounded daily, r = 5% or 0.05

• FV = $1284.00

If you wanted semi-annual interest, then t = 2.  For monthly interest, t = 12.

Upping the Ante

Now I know that there are many calculators available just a few key presses away on the Internet that can perform the above examples.  Indeed with a little effort, you can find calculators for more complex problems.  However the benefit to performing these calculations yourself is that you can adapt to far more complex scenarios.

Starting simple, at what age will a 16 year old have an account balance of $1,000,000 if $100 is deposited every month earning 8% interest compounded monthly?  While we could derive an equation to solve for time and get the answer directly, I want apply our current equation in a spreadsheet because of the adaptability.  First two columns are used to track month and age.  Then a third column labeled Start Month adds $100 to the account balance.  A fourth column labeled End Month displays the account total with the compounded interest.

Looking at the spreadsheet pictured below:

• C2 = $100
• D2 uses the following values for our formula: PV = C2 (e.g. $100), r = 0.08, t = 12, n = 1
• C3 = D2 + $100
• D3 repeats D2 except: PV = C3 

Every row following C3 and D3 simply increment the equations found in those two cells.  Continuing on the answer is found in row 633, when our 16 year old is now 68 in the month of August.

Let's add an infinitesimal amount of complexity.  Keeping everything the same except the following: the 16 year old only invests $100 per month for the first 10 years.  At what age will the account balance be greater than $1,000,000?

Here is an example of why I like using a spreadsheet.  For the initial 10 years, our spreadsheet is unchanged.  In January of our subjects 26th year, we change the C column to reflect that we no longer add $100 per month.  Thus C122 = D121, and all cells onwards from C122 simply equal the D cell from the prior month.  (e.g. C130 = D129)

Continuing on the answer is found in row 721, when our 16 year old is now 75 in the month of December.

Finally a comparison exercise: at what age will a 35 year old have an account balance of $1,000,000 if $400 is deposited every month earning 8% interest compounded monthly?  The answer is at the end of the article.

Summary

In today's Learning from the Ground Up, you were given an introduction to Time Value of Money.  You should now be able to:

• Calculate simple interest.
• Calculate compound interest.
• Adapt the time value money formula for different financial scenarios

Final Thoughts

Time is money or time earns money - Ultimately, it really depends on whether you're borrowing or saving AND the length of time interest accrues.  

Interestingly while googling the quote at the beginning of this article, I ran across snopes.com where they cannot confirm that the famous physicist ever did utter these words.  None-the-less I completely agree with the sentiment of the quote.  

And the answer is:

when our 35 year old is now 70 in the month of November.  This illustrates one final important point, start investing early. 

Disclaimer: Please remember that I’m just a guy sharing information on a blog, and this is NOT official investment advice. Any action that you take as a result of information, analysis, or advertisement on this site is ultimately your responsibility. Please consult your investment adviser before making any investment decisions. During your conversation with said investment adviser, ask why they believe in their recommendation. If you are not convinced by their explanation, any action that you take or forego is also your responsibility. Just in case you missed that, you are responsible for your investments.

With that said, don’t let your investments keep you up at night. If they do keep you awake, you may be taking more risks than you are comfortable with. Talk to a professional about reallocating to less risky investments so that you can sleep. During your conversation with said professional, ask why they believe that their recommendation is less risky. If you are not convinced by their explanation, don’t invest. Remember:

1. It’s your nest egg.
2. Opportunities are easier to make up than losses.