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Time Value of Money

Time Value of Money

 - Introduction
 - Time Value Tables
 - Introducing the HP12C
 - Tricks to Watch out for 



Introducing to the HP12C

The HP 12C business calculator makes understanding and using the Time Value of Money concepts very easy. Investors should understand how to use this calculator. For many years the HP 12C was the gold standard of business calculators. Today there are more choices, such as modern menu driven financial calculators, and programs like Excel and TValue; these are excellent tools and I suggest you learn how to use them. I’m using the HP 12C as the example, as it is what I use. The HP 12C is quick, easy, durable and portable. It’s also inexpensive and when the kids drop it, it doesn’t break. Learning how to use this calculator will reinforce the time value of money concepts.

Picture courtesy of Hewlett-Packard Development Company, L. P.

There are basically ten keys which one needs to understand; they are as follow:  




The time period, usually in years or months


The interest rate, the time periods and interest rates must be comparable


Present value or today’s value


Recurring payment amount


Future value

f  (Gold Key)  CLX    

Clears calculator (the combination of pressing F (Gold Key) followed by CLX)

g  (Blue Key)     

Changes calculator to the blue keys

g   Beg
(7 key)     

Cash flow starts in the beginning of the period. If you ever rented an apartment, you pay in advance of moving in

g  End
(8 key)      

Cash flow start at the end of the period (In arrears)


Changes signs to positive or negative cash flow 

Let’s discuss the concepts by using hypothetical examples and assumptions. These examples are used solely for the purpose of learning how to use the calculator and understanding time value of money concepts: 

Calculating Future Value:

You are 22 years old and have $10,000 to invest with a 50-year time horizon (yes; that is how long you will be working). You know of a stock or mutual fund that has an historical 10 year return of 8% and feel that the investment could return the same over the next 50 years (good luck – I can’t predict next year, much less the next 50!). That said, how much could you anticipate having, assuming no more payments, when you retire in 50 years?

$10,000 today invested over 50 years at a hypothetical return of 8% = $469,016. Outlined below are the HP procedures:

Enter:   f “gold key” – CLX [clears the calculator’s memory]
  g “blue key” – end (the 8 key)  

Enter:   50 –Press “n”
   8 – Press “i”
   10,000 – Press “CHS” and then “PV”
   FV = $469,016 

Making Quick Changes:  Now suppose, (using that same amount and rate) you delay your initial investment until you are 47 years old. Your investment term, therefore, would be 25 years. How much can you expect in 25 years?

Enter:   25 –Press “n” (Only change term, and recalculate FV)
   FV = $68,485.

Look how your projected future value dropped from $469,016 to $68,485; by reducing your savings period. A 50% reduction in time reduced your projected future value by 85%!

The critical advantage that young investors have, is that time is on their side.

The nice feature of the HP 12C is that making scenario changes is easy and fast. The calculator stores the data and only changes need to be inputted.

Calculating the Future Value of Annuity Payments: Let’s use another hypothetical example; make annual payments of $2,000 at the end of every year for 50 years at a hypothetical 8% rate:

Example of annual payments:

Press:   f – “gold key” CLX [clears the calculator’s memory]
   g “blue key” - end (the 8 key)

Enter:   50 – Press “n”
   8 – Press “i”
   2,000 – Press “CHS” followed by the “PMT” key
   FV = $1,147,540

Making Quick Changes: Example of monthly payments of $166.67, the beginning of each month:

Example of monthly payments:

Enter:   50 – g “blue key” – Press “n”
   8 – g “blue key” – Press “i”
   0 – Press “PV”
   166.67 –Press “CHS” and then “PMT”
   FV= $1,321,981

I’m emphasizing, all things being equal, that regular monthly savings throughout the year is more valuable then a lump sum year-end contribution.

Another Example of Future Value Annuity Payments:  Assume you work for a company and your salary is $50,000 per year. The company matches 50% on the first 4% of your 401k contributions. The company also allows for an additional 10% non-matching contribution, resulting in a total annual contribution of $8,000. Invested at an 8% rate, after 50 years, assuming no salary raises, your 401k balance would equal $4,590,161. This is the beautiful part of the time value of money concept.

Because individuals are now living longer, the time value of money works to their benefit. Remember, this is just an example in understanding the time value of money concept. The return percentages used are just hypothetical examples.

Pre-tax versus after-tax returns will be discussed later.

Calculating Payments:

While I’m reviewing the benefits of a financial calculator, I would like to do one real estate mortgage example. For this exercise, let’s use a $150,000 mortgage, with a 6% interest rate, paid monthly for 15 years. To determine the monthly payment, here are the HP procedures:       

Press:    f – CLX
   g – END (1st Payments in arrears

Enter:   15 – g – n (converts years to months)
    6 – g – i (converts the 6% annual rate to a monthly rate)
    150,000 – CHS – PV
   PMT = $1,266 (excluding property taxes)

Making Quick Changes: Now let’s calculate the payment of a 30-year mortgage:

Enter:   30 – Press “g” and “n”
    PMT = 899 (excluding property taxes)

In this example $367 [$1,266-$899] per month of additional payments will reduce the mortgage tern by 15 years. When possible, I highly recommend a 15 year mortgage. A shorter term 15 year mortgage substantially reduces the interest that is paid to the bank when compared to the conventional 30 year mortgage. Here’s how:

Total payments on a 30 year mortgage 323,640
Total payments on a 15 year mortgage  227,880
Pre-tax cash flow savings                         95,760

It would take the average young adult over a decade to save $95,000.

Calculating Interest Rate:

Finally, it’s important to discuss at least one interest rate example. Assume that you won the million dollar lottery, and were offered $50,000 pretax, per year for 20 years, or a lump sum, up-front, pretax payment of $530,179. How do you determine which option to take? The first step is to determine what discount interest rate is being used by the lottery. Then it’s a function of comparative shopping. Is the interest rate being offered by the lottery better or worst then similar market rates?  Here are the HP procedures to solve for interest:

Press:    f – CLX
   g – BEG (1st Payments in advance)
   20 – Press “n”
    530,179 – Press “CHS” then “PV”
    $50,000 – PMT
   i = 8%     

Some issues are individual specific. If you need the money, take the cash upfront. If however, you want the annuity, you should calculate the discount rate used (in this case 8%) and then determine if a better (but credit equivalent) market rate is available to you. Using after-tax dollars is a more accurate technique. Nonetheless, now you have the information and skills needed to make a more informed decision, as to taking your winnings upfront or over time.    

Next review:  Tricks to Watch out for.


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