Apples & Oranges

In my newly-minted capacity as a financially-responsible person, I’ve been reading a lot of personal finance blogs and other resources. And there’s one very big point that everybody seems to be missing — “present value” or “the time-value of money”. It was the first and most important lesson in my university’s Intro to Finance class, and something that needs to be in the back of everybody’s mind, especially when they’re talking about money over long periods. Otherwise, you’re not comparing apples to apples.

Essentially, a dollar today is worth more than a dollar next year. (Or, Helga, if you’re in 1920’s Germany, a mark today is worth more than a mark in 10 minutes.) The cause is inflation. If your dollar buys a loaf of bread today, and bread inflation is 5%, then that dollar will buy only 95% of a loaf next year, 90.2% the year after, and 85.7% in two years, and 59.8% in 10.

Alternatively, you could think of this in terms of the opportunity cost of holding money. Lend me $10,000 today, and I’ll be more than happy to pay you $10,000 in ten years; I’ll have made about $15,0000 in the meantime. Of course, you could make the same $15,0000 for yourself. So what’s today’s value of $25,000 in 10 years? About $10,000. What about $25,0000 in 20 years time? Just $3,700 today. Without equalizing them somehow, trying to compare $25,000 today, in 10 years, and in 20 years is futile.

(Above, I was using the opportunity cost of what today’s money could be worth to you in the future based on a 10% yearly return. When thinking in present value, though, it’s best to use what today’s money will be able to buy for you in the future, or the inflation rate. I’ll be using 4% for inflation from here on out.)

So, in practical terms, what does this mean?

  • Well, first of all, that million dollars your retirement calculator says you’ll have in 2035 won’t be worth a million; it’ll only be able to buy what $333,000 would buy today.
  • On the other hand, the $2,500 a month that you’re paying in mortgage for the next 30 years? It should only feel like $770 in your last year.
  • And — this is the crux — you just can not compare two values by looking at what their numbers in different periods. Anybody attempting to prove a point by doing so is misleading at best, or dishonest at worst.

My next post be walking through an example the most egregious violator I’ve found (and the reason I wrote this article), Vanguard.

But if you’d like to calculate present value, it’s quite easy; it’s the reverse of the formula for compound interest. To find the present value of a sum in the future, you start with the rate (i), how many years into the future you have that sum (t), and the amount you will have (Ct). Then, it’s simply:

C = Ct / (1 + i) ^ t

What is your future $100,000 in your 2017 savings account really worth?


C = Ct / (1 + i) ^ t
C = 100000 / (1 + .04) ^ 10
C = 100000 / 1.4802
C = $67,558