There has never been a time to be a debtor than today.

Rates are at record lows, and valuations in most every investment vehicle are larger than I would have otherwise expected, an implication that investors are still in “risk-off” mode.

### Dissecting Time from TVM

Finance has two components, time and money. As the time value of money equation is fairly to navigate for anyone with any algebraic skills – or anyone with a copy of Microsoft Office – it is easy to multiply and divide to break down the time value of money to solve for different pieces of the equation.

Too often I feel as though the personal finance blogosphere gets caught up in total interest costs. That is to say that people are far too interested in the total dollar cost of debt, particularly in long-run borrowing mechanisms like the 30-year mortgage. Any amount financed at any interest rate for a period of time as long as 30 years appears to be quite large given that interest does grow exponentially with respect to time.

Seeing as we’re keen on taking out of context comparisons between the true cost of debt over time, let’s reverse the equation so that we can calculate the true cost of time over an interest rate. I’ll muck up the math so that I can come to a conclusion that agrees with my thesis so as to follow along with the requirements of consistent personal finance blogging.

### A Prime Example

I recently saw a tweet about how car buyers in the early 1980s paid 12% or more for an auto loan, yet borrowers almost always paid off their cars in less than three years. Today, rates find new lows as each day goes by, and the average car loan is paid off after a period just a tad longer than 60 months. Bankrate says the average car loan originated in 2009 would be paid off in 60-some odd installments, down from nearly 70 installments in 2008.

This chart shows how very high the Prime rate was in the 1980s and how low the Prime rate is today:

Today you can finance a new auto loan for mere pennies. The rate in my local area is roughly 3% for a 60-month new auto loan. In the 1980s, that same loan would have an interest rate of 12% or more for a 36-month arrangement.

A $20,000 car financed in 2011 at 3% for 60-months would bring payments totaling $21,562.43. A $20,000 car financed in the 1980s at 12% for 36-months would cost $23,914.30.

**Comparing the Two Loans**

In comparing the two, we find that a car loan at 3% for 60 months costs $1,562.43 in interest. The same car financed at 12% for 3 years would generate an interest expense of $3,914.30.

We can solve for time to conclude that today, two units of time in 2012 must cost 60% less than a single unit in 1980.

If you care:I broke the mathematical rules most commonly broken by personal finance enthusiasts above – dividing into an equation without paying respect to the exponents in TVM (time). Purists should know $20,000 at 3% for 3 years generates an interest expense equal to $938.47, roughly 30% the cost of a loan of the same duration in the 1980s. Shh! Don’t tell the secret – you can “prove” most any financial “thesis” backing the immediate repayment of debt by breaking basic math rules. (In this case, it pays me no large favor, anyway.)

Obviously it makes sense for borrowers to stretch payments for as long as possible. Just as you receive nearly twice the quantity of Wendy’s fries when you opt to “Biggie size” your meal for a proportionally smaller additional cost, you get even more discounted time when you add it to a car loan.

So, who’s the real fool? Is it the one who passes up inexpensive time – something so many people claim cannot be purchased – or the one who passes up time in lieu of total interest savings?

Money isn’t the only thing on sale. There’s a blue light special on time, which can be found next to the financial fountain of youth. See you there!

{ 9 comments… read them below or add one }

Yeah it always boggles my mind to see PF bloggers add up all the interest paid on a mortgage and say “Look! You’re paying for your house twice!” or whatever other nonsense. It’s even funnier when they say, “No, don’t invest the money, pay off your mortgage – look at all that interest you’ll save!” as if the cost of any interest automatically outweighs the proceeds from any investment.

This is exactly why I dislike the term “personal finance” because the “finance” part is almost always rejected as textbook nonsense that has no practical application.

Try as anyone might, I fear it will be impossible to reverse what has become so ingrained into common thought. Very simple divergence from a rules-based, illogical approach to finance will make most anyone wealthy. I’m convinced that all you need to become a millionaire is an understanding of exponential equations, and the ability to see and measure opportunity costs.

*Stepping on my soapbox for a moment.* Most errors I see are:

1) Ignoring opportunity costs, like you mentioned.

2) Ignoring that which is not certainty, and concluding that expected returns from debt repayment are the only possible choice.

3) Ignoring the relationship between time and money by comparing two choices with different horizons. (Example: Savings obtained from knocking 10 years off a 30 year mortgage to the returns on an alternative investment over the course of 20 years.)

4) Big number paralysis, AKA “paying for your house twice!” Stick to percentages, and ignore the total dollar cost, unless it is a minute amount of money. Pretty simple fix here.

I used to think we should teach personal finance in high schools and colleges. Now I’ve come to the conclusion we should just teach finance. No personal nonsense, just finance. It’s really just algebra, but I think dollar signs are like an anti-IQ or something. I know plenty of people who are at least 100x times better with numbers than I am, yet I can burn them on anything that starts with a dollar sign. It’s weird. Conversely, I’m worthless when there is no dollar sign. 😛

The $20,000 car in the 80s would have been a sweet piece of machinery too. Of course, quality improvements all over would probably mean that same car today would be worse off, technology wise, than the $20,000 2012 car. But, relative to the market, the 80s car would stand out.

I think there’s an easy point to make here… if the Government is encouraged to inflate in the future, it will probably do some inflating! Inflation is a massive help to debtors, especially those with a fixed rate debt.

Ha, yeah, a $20,000 car in 1980 would be ballin’ for sure. Sad to say that $20,000 doesn’t get you all that much in a car any more.

I’ll take all the fixed-rate debt that I can get. Seriously. I’ll borrow any amount of money at a fixed interest rate for the next gazillion years. So long as it is a meaningful sum, and a meaningful duration (10 years, minimum) sign me up for any amount of capital you have to lend!

You’ve inspired me to write another post on a similar, but different topic re: inflation.

You might want to set an interest cap on that…no matter how certain you may be that inflation will occur, you probably don’t want to take the 100-year loan I’m offering you right now at 100% interest. As much as you’d like. I won’t even ask you to amortize it!

Caught me! You’re right, I don’t want that 100% loan. I’ll take it at the current rate for Treasuries + 2%. 😉

Good analysis, JT. Even intuitively, a leverage-to-the-eyeballs strategy isn’t easy to discount. The Fed has stated repeatedly that ZIRP is here to stay for the near future.

I love ZIRP. Free money, baby!

This is fantastic. Ignoring opportunity costs and inflation are the biggest errors I see.