Sat 14 Oct 2006

**Who:** This post is for folks who aren’t scared of a little math. Also, if you’re interested in learning some metrics to evaluate different financial options that span various time period, you’ll like this post.

** What:** This post discusses the time value of money, as you may have guessed. The post will discuss how money grows and fundamental concepts about evaluating monetary offerings.

[Note: This post may contains content that may be highly objectionable to those who don’t understand middle school level mathematical concepts. Parental discretion is advised]

The concept of Time Value of Money is a simple yet essential concept that *everyone* who is a participant of A Financial Revolution must master. The idea is simple and intuitive, but its applications are often overlooked.

Would you rather have $1 now, or $1 later? Of course, most of you would take $1 now and would be correct in doing so. But why? For the most part, the real reason lies in what we call the **risk-free rate**. The risk-free rate is the rate of interest you get on your money with no risk (it’s actually minuscule risk, but technically not 0). The existence of a risk free rate means that money that you get now can “work for you” and generate interest for you in the future. It also means that money given to you in the future, has less value right now because you *can’t* let it work for you and accrue interest.

This brings us to the concepts of **future value** and **present value**. Future value is simply a calculation of what current money will be worth in the future and present value is the current value of money that will be given to you in the future.

Let’s do an example. For simplicity, let’s assume the risk free rate is 5% per year. The question is, would you rather have $1000 today or $1020 in one year? For this, we want to find the present value of both of these

cash flows.A) The present value of $1000 today is… you guessed it, $1000.

B) The present value of $1020 one year from now is found using the following formula:p = A / (1+r)^y

p is the present value, A is the amount you are being given, r is the risk free rate (.05) and y is the number of years in the future you are receiving the amount. In this case we have p = 1020 / (1 + .05)^1 = $972.43

So, looking at the present values of both cash flows, we find that the first cash flow is better. After all, $1000 is more than $972.43, right? All this problem tells you is that $1020 a year from now would be worth $972.43 today. In other words, if you wanted to have $1020 in one year, you’d need to invest $972.43 at 5% today.

Now, for a future value problem. Which will be worth more in 5 years? Someone giving you $1000 today? or someone giving you $1075, 2 years from now?

A) The future value of a cash flow:

f = A * (1 + r)^y

Looks simple, right? It is. Just changing the division to a multiplication from the last formula. So, if someone gave you $1000 today and you let it sit for 5 years at 5%, you would have:

f = 1000 * (1 + .05)^5 = $1276.28B) Since you would be receiving the $1075 in 2 years, it’d only get to compound for 3 years!

f = 1075 * (1 + .05)^3 = $1244.45

Voila, now you know that you’d choose option A and take the $1000 right now. For some of you clever folks who wanted to use the first formula, indeed you could have just taken the present value of $1075 to see that it came out to ~$975, which would tell you that the $1000 today would be a better option!

Now that I have bored you with all the gory details, (Well, some of them) I know you’re asking SO WHAT? Why does this matter to me? First, I will quantify the risk-free rate for you. For you, the risk-free rate is the highest rate of interest paid by an investment vehicle available to you. Is your local bank offering a 5.2% CD rate? Do you have an online savings account at E-Loan paying 5.5%? So, right now, enumerate all the options that are available to you and their interest rates.

It’s ok, I will wait…

Done? Good. Now, do a quick browse and find the highest one. That interest rate that is *easily* and *readily* available to you is your risk-free rate. Now that you know your risk free rate, you can evaluate any financial offers that you receive. What does all of this mean?

- That $300 you keep under your mattress could be invested right now to earn you money. By not investing or saving money, you aren’t just preventing yourself from making money, but you’re LOSING money.
- Every minute you waste, dawdle, or make excuses, you are preventing yourself from taking advantage of the time value of money.
- If you’re paying a very low interest rate on a loan (rare occasion) or other outstanding debt, and this rate is lower than your risk-free rate, then you’re actually MAKING money on the loan. Keep it as long as your risk-free rate is higher than the loan rate!! (A lot more on this specific topic in future posts)

I’ll be referring to this post in the above-referenced contexts and much, much more, so always keep this concept in the back of your mind. If you don’t remember all the mathematics of it, that is ok, but I definitely suggest being comfortable with the generalized concept.

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