Saturday, November 23, 2024

This is a tricky question so please read through the entire answer. It's this type of "fuzzy math" that can end up costing people a bundle!

QUESTION: Which loan is better and why?

Loan 1: $100,000.00, 30-year loan, with monthly payments of $665.31. That's a total out-of-pocket cost of $665.31 x 360 months = $239,511.60.

Loan 2: $100,000.00, 15-year loan, with monthly payments of $1,014.27. That's a total out-of-pocket cost of $1,014.27 x 180 months = $182,568.60

ANSWER: Loan 1 is better because it really does cost less!

Let's pretend that I already have loan 1. Now imagine having a mortgage broker trying to sell me loan 2 to replace my loan 1.

Here's the pitch. "Scott, listen, if you do a 15-year mortgage with the $1,014.27 monthly payment, you'll save $56,943.00! Just sign here!"

Is the broker lying? Well, not technically, however it is true that loan 2, even though it "seems" like it saves you money, is actually more expensive!

Even under the sales pressure I would go get my calculator to figure out the most important cost for any loan, the interest rate (APR).

It turns out that Loan 1 is 7% and Loan 2 is 9%. I used the DebtSmart Loan Calculator to get the rates. Use this link to find out how you can get the calculator: http://www.debtsmart.com/offers/p_debtsmart_calc.html

Armed with that information, I'd say to the mortgage broker, "Why would I want to use the 15-year, 9% loan over the 7% loan?" To which the response is, "Rate doesn't matter, you save $56,943.00! Scott, are you trying to tell me that you don't save $56,943.00, are you saying that I'm a liar!"

He's not lying. It's true that loan 2 does save $56,943.00 over loan 1.

So then, how is it better to use loan 1? How can loan 1 possibly be cheaper when it is true that loan 2 saves $56,943.00?

Fuzzy math!

It's an unfair math comparison. A trick question. It's not an apples-to-apples comparison because the monthly payments are not equal!

I would say to the broker. "Rate does matter. If I can afford to make a $1,014.27 monthly payment to loan 2 then I can afford to make the same payment to loan 1. When I do that I can pay off loan 1 in 12.27 years. Which is obviously much shorted than the 15-year option. In fact, if I did that I can pay off loan 1 with a total of $149,341.11. That pay off figure is $33,227.49 cheaper than the 15-year option!"

At that point the mortgage broker would either act confused, because he doesn't get it, or look surprised that you figured out his fuzzy-math game.

The main key to comparing loans is being sure that the comparison is fair. That means that you can only have one parameter change and all others held constant. To make a fair comparison in this case the principal ($100,000) and payments must remain the same for both situations. The change is in the rate (7% or 9%). Keep in mind that the repayment-times change however, it's because the repayment-time is a function of the principal, rate, and payment.

Once we make the fair comparison, it's clear that loan 1 is the better, cheaper loan.

Quick mention...many people did respond and say that loan 1 was better because you can use the difference between the payment for investment purposes.

Of course, you need to know the interest rates before doing the investing since to make the investment worthwhile you'd need to make the same rate as the loan cost just to break even. However, thinking about "using the difference between the payments" is a clear sign that there's extra money floating around. That extra money is a symptom of the "fuzzy math".

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