How much is a trillion anyway?
I don’t know about you, but I’m starting to lose the awe I first felt when I heard the number “one trillion.” The number has been thrown around so much with the stimulus plan, various bailouts, etc. that it is easy to forget how large that number truly is. Let’s see it written out, just to see how impressive it looks:
I would like to recast it a few different ways. For example, Jesus Christ was born something over 2000 years ago, although the exact date is not known. Let’s assume that December 25th, 2008 really was His 2008th birthday. This equates to approximately 733,422 days, depending on leap years, historical changes etc. (I simply assumed 365.25 days per year). Since that was 69 days ago, we are now at 733,491 days since His birth.
I’m going to round it off and call it 734,000 days. If you opened a business on day 1, and lost $1.36 MILLION every single day since then, you would have lost $998 billion, or basically $1 trillion.
Another way to think about it is that there are 300 million Americans (in round numbers). So, $1 trillion is just over $3,300 for every single American. That doesn’t sound as big, does it?
Or how about this? Assume your heart beats 75 times per minute, and that you live 75 years, which is roughly the average life expectancy in the United States. You would have to spend $338 per heartbeat to reach $1 trillion in your lifetime.
What do you think? Do you have a different way of getting your head around the concept of a trillion? Let me know in the comments if you do.
EDIT — A number of people told me they would like to see this type of thing as a separate category, so I’m filing it under number freaking instead.
Mortgage Bailout Math
I’m not sure if mortgages is the right category for this, but I have to put it somewhere, so I’ll put it here.
A lot of friends have asked me what I think about the various bailouts, stimulus plans, etc.
I agree with many people, that they simply won’t do what they are being touted to do, and at the same time are way too expensive. Instead, I have an alternate plan for the $750 billion spent to bail out the mortgage crisis:
1. There are approximately 55 million households with a mortgage in the United States.
2. Let’s estimate that 10% of these are in some form of default, but that ultimately 20% of mortgages will fall into that category.
3. Let’s take the $750 billion as a given, in other words, if you wanted to spend that much to fix the problem, what would you spend it on.
Simple arithmetic tells us that we could pay approximately $13,600 on the mortgage of every household in the country. Not pay the homeowner, but pay it on their behalf to their mortgage lender. Wouldn’t this solve the problem far more effectively, and for the same price? Yes, I realize it is a bad idea, and I am half joking in proposing this, but isn’t a bad idea that accomplishes its goal better than a bad idea that doesn’t?
Alternatively, we could pay just over $68,000 on the mortgage of everyone in or near default (the 20% mentioned above). This has the benefit of helping where the situation is most dire, but is also completely unfair to those who are current on their mortgages. Not to mention those that don’t even have a mortgage, whether they rent or have paid theirs off.
Maybe there is a happy medium where we can focus some money on those who are in default, while still giving a handout to those who are current or don’t have a mortgage.
So let’s try again, but with different numbers. Take the $750 billion bailout, and add the $787 billion stimulus plan and get $1.537 trillion. Then pay $25,000 on the mortgage of anyone in or near default (11 million homes) which uses up $275 billion. Give the government a lien of $25K on each home, to be paid out of any profits when the house is sold, or forgiven if the home is sold for a loss.
This leaves $1.26 trillion to spread among the other 89 million households in the country, or just over $14,000 per family that is not in default.
So, if you are in or near default, you get $25K, but it gets paid to your lender, not you and gives the government a lien when the home is later sold. If you are current, or don’t have a mortgage, you only get $14K, but it is unrestricted cash that you can spend, invest or burn to heat your home.
This proposal is utterly ridiculous and would never happen, but it still makes a lot more sense than the plan that did pass.
Why thirty years is the default for mortgages
This is the first post on mortgages, and I hope it highlights the kind of analytical approach I’d like to take on this blog.
A few months back, No Debt Plan took a look at fifteen year versus thirty year mortgages. There was a lot of discussion and debate on the topic, and No Debt Plan came down on the side of a thirty year mortgage, as it allows more flexibility in your monthly payment.
One of the issues that came up was why the default option is thirty years anyway. One commenter asked why not forty? Why not fifty?
I think there are two good reasons why thirty years is the default mortgage length, and I will address both, but my primary focus will be the second one.
The first reason is that thirty years is a reasonable proxy for a working career. Get out of school, get a job and save up for a few years and buy your first home in your late twenties or early thirties. A thirty year mortgage would then be paid off around your 60th birthday, which is when many people hope to retire. A forty year mortgage would not be paid off until you are in your 70s, which is not realistic for most people.
The second, and more interesting, reason is that the benefit from extending the mortgage term drops off quickly after 30 years, as shown in the following chart. which uses $100,000 as the loan amount and an interest rate of 6%.
I/O is an interest only loan, which is mathematically equivalent to an infinite term loan. It sets the floor for the lowest possible payment for a given interest rate. One thing to note is that lenders typically charge a higher rate the longer the term of the loan. This next chart shows what happens when the interest rate is 1/8th of a point higher for each additional five years of term (starting at 6%) for a fifteen year loan. This shows that the benefit from extending the loan is even smaller as you get out past thirty years.
I think these charts illustrate that the selection of 30 years is not an accident, and is based on a balance between a low payment and a reasonable term. After thirty years, there simply is very little benefit to extending the term, especially if you have to pay a higher rate for doing so.
As a borrower, what should you do? In general, I agree with No Debt Plan – unless the interest rate is significantly lower for a fifteen year loan, go with the thirty and commit to paying the difference in extra payments to pay off the loan faster. That way you still may be able to pay off the loan in fifteen years, but if a financial emergency strikes, you have the flexibility of a lower payment. However, if you don’t think you will actually pay extra, it may be wise to get a fifteen or twenty year mortgage, so that you are forced to pay it off more quickly.
What do you think? Does taking a thirty year loan with the intention of paying it off more quickly just set you up for failure? Is it better to commit to a quicker payoff, since that commitment will make it more likely that you actually do it?
Welcome to Finance for Nerds
Have you ever read a personal finance book and wondered where the details were? Have you ever wished that you could really dig into the math behind personal finance? If so, this is the site for you.
Rather than talk about boilerplate personal finance issues, I hope to really get into the meat of the topics, and provide valuable advice and insight. This site is for those people who are quantitatively inclined, but want help applying those skills to their personal financial situation.
We will discuss the math behind compound interest, whether a 15 year or 30 year mortgage is better, and many similar topics. Please feel free to post comments, and let me know what other topics might interest you!
Finance Nerd