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!