More than a year ago, Connie wrote a column for us on the importance of remembering two key concepts that we were taught in school but that we may have forgotten: percentages and percentage change.
This week, as I perused yet another dubious pitch from our bank -- and had a familiar debate with my husband over whether this particular refinance offer was worth considering -- I was reminded of another mathematical concept that can easily get left behind: the time value of money.
Unlike percentages and percentage change, the time value of money isn't, as rule, taught in school, although some high schools do have financial literacy courses that include it. I’m not going back to school any time soon, but my kids recently have. The time value of money is one thing I really wish they’d learn there, although I suspect I’ll end up teaching them myself.
The time value of money is something that we understand intuitively. Most of us have heard about the so-called “marshmallow experiment,” in which a three-, four-, or five-year-old child is put in a room with a marshmallow. The researcher prepares to leave the room and tells the child that he or she can have two marshmallows if the child can just wait until the researcher gets back. Then the clock starts ticking, and we find out how long the kid can wait before scarfing down the marshmallow.
The kids who wait longer are said to have better executive function. We accept that the ability to resist temptation, at least for a while, is a sign of maturity. We also accept that if you wait longer for something, it’s somehow fair that, when your time finally comes, you get more of it.
The flip side: If you’re getting something now that you weren’t scheduled to get until later, you’re entitled to less of it.
This relationship between time and value becomes even clearer if we replace marshmallows with money. Marshmallows don’t earn interest and can’t be invested; money can. Money today is worth more than the same amount of money tomorrow. If we’re going to have to wait to get our cash, we should get more of it. Or at least an extra marshmallow.
Theoretically, it seems fair. But when we suddenly find this idea actually enshrined in our legal system and on Wall Street, it can seem suddenly, outrageously, unfair. Which is why it’s so important to understand what's going on here before agreeing to be bought out of your lottery ticket or other long-term contract. Or deciding it’s a good idea to refinance your house. These aren't things you want to screw up. So bear with me.
Take the refinance offer. I’m going to simplify it a bit, but you’ll still get the idea. The bank promises us we’ll save $20,000 over 20 years if we refinance. Let’s say we’re going to pay $5,000 in closing costs. We come out ahead by 15 grand, right?
Wrong. We have to pay the $5,000 now. We get the $20,000, but we have to wait 20 years before we get all of it. So how much is that $20,000 worth in today’s dollars?
Let’s say, that, over 20 years, we think we can average a six percent return on money we invest. Let’s also assume that, by refinancing, we save $1,000 per year for 20 years. The $1,000 we get at the end of the first year is actually worth $943.40 in today’s dollars, because if we invested $943.40 for one year at six percent, we’d have $1,000.
The $1,000 we save 20 years from now is actually worth much less, because to get $1,000 in 20 years, we only have to invest $311.82 today. You can figure this out by dividing 1,000 by 1.0620. Don’t worry: There’s a button for that. To figure out 1.06 to the power of 20, simply type “1.06,” then press the yx button, then “20.” You’ll get 3.207.
If we figure out how much the $1,000 is worth in each of the 20 years, and then add those numbers together, we’ll know what that $20,000 is really worth -- in today's dollars -- if it's doled out over 20 years.
It’s $11,473.89. That’s a far cry from $20,000.
That may still make the refinance a good deal. But we won’t save $15,000, as it first appeared. In today’s dollars, we’re saving $11,473.89 minus the $5,000 in closing costs, which equals $6,473.89.
That’s why lotteries generally pay out over 20 or 30 years, and why people who opt to get the whole thing as a lump sum get much less than the headline-grabbing number that gets bandied about (although no doubt, it’s still a lot of money).
I don’t know if you get as many refi offers as we do, but I hope you look at them carefully before calling the bank. I hope you or a teacher explains this to your kids and friends. And I hope you get to save more than $6,000! -- Kimberly Weisul
September 11, 2014
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Math That Matters
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Lilly Ledbetter, Equal Pay for Women, and Toyo Tires
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I do quite a bit of freelance writing, as does a good friend of mine. One of our regular lunch conversations begins, “You know, that piece went really well, but in end the client….”
Generally, the client reached out, complained about a paradigm shift, circled back with his subject matter expert, and wanted us to repeat the key takeaways.
Often that's fine. As a writer, I want my work to be clear and concise. As a businessperson, I have to respect the fact that sometimes, that's not what the client wants.
Every field has its own jargon, of course, but some terms are awful enough to transcend mere industry. Here are a few that deserve to be banned.
The poor wo/man’s substitute for “in agreement with.” People who are aligned with each other have the same relationship as planets that get into alignment – everything looks pretty, but in reality, they’ll never get within spitting distance of each other’s actual positions.
I remember when Katarina Witt won her two gold medals, but just barely. I didn’t really appreciate what was different about her skating, aside from the jumps. I could certainly see why men liked to watch her, but that wasn’t what the Olympics were supposed to be about. Was it?
So I was a bit skeptical upon learning that I would get to hear Witt speak at the We Own It Summit in Philadelphia in May, and then would have the opportunity to sit with her for a private interview later. I shouldn’t have been. It soon became clear that no matter what Witt chose to do, she would have been successful –- but it happened to be skating, and it landed her on a international stage and granted her worldwide celebrity.
It was great fun to speak with her and hear her talk about her competitive nature and her perspective on feminism: “I always grew up thinking women, we make more money; men, they do the cooking. So it’s equal.”
Here are some highlights from both conversations.
On how she became a skater:
At the arena, at the kindergarten, I somehow fell in love with skating. I was begging my parents that they would bring me there and introduce me to the coach. My very first coach went to my mom, and he says, “Just bring her. I cannot promise you a world champion, but just bring her back.”
Luckily I had the best coach in the world working there. She started to work with me when I was nine. I realized she was the best coach in the world and I was ready to take that challenge.
It’s the time of year when notables share their wisdom with college graduates, in the form of commencement addresses. Unfortunately, most of these speeches are sort of boring and trite: Do what you love. Dream big. Work hard. Never give up.
Every once in a while, though, a speech stands out. We called out some of the notable ones in "Wit, Wisdom, Wisecracks and Sunscreen." Among them: the pitch Apple CEO Steve Jobs made in 2005 to Stanford University students on living every day as though it was their last; J.K. Rowling’s 2008 address at Harvard University on facing your fears to survive and thrive; and British Prime Minister Winston Churchill’s 1941 call to arms before World War II, which gave life to the famous line, “Never give in.”
Thanks to Admiral William H. McRaven, we’ve now got another one to add to the list.
McRaven, who has been a Navy SEAL for 36 years, addressed graduates at the University of Texas at Austin last week. In a little less than 20 minutes, he offered up some of the pithiest advice graduates -- or the rest of us -- are likely to get any time soon. As of this writing, the YouTube video of his address has been viewed nearly a million times.
His big theme was that it’s easier than you think to change the lives of people around you. Even small decisions can have big consequences. Noting that a soldier’s decision to take a left instead of a right down a Baghdad road saved the lives of a 10-person squad, McRaven talked about how that decision spared the families of those soliders from great pain – and also affected future generations.
How I need a drink, alcoholic in nature, after the heavy lectures involving quantum mechanics.
If you’ve read that sentence before, you’re a better geek than I.
So-called Pi Day, celebrated on March 14, is almost upon us. That sentence is the best-known example of a form of writing called, appropriately, Pi-lish, which is designed to help you remember the digits of the number pi. If you count the letters of each word in that sentence, you’ll have recited pi out to 12 decimal places.
Pi, of course, is the so-called circle constant, represented by the Greek letter of the same name. It’s defined as the circumference of any circle divided by its diameter, or roughly 3.14159.
Pi appears repeatedly throughout geometry, but also, says Ron Hipschman, a scientist at San Francisco’s Exploratorium, “anytime you have cycles, frequencies, or anything that’s rotating. It’s in tons of different places.”
Pi has been calculated to 10 trillion digits, and counting.
In 1988, the Exploratorium’s Larry Shaw, a physicist, thought pi deserved a holiday of its own. So on March 14 (3/14) he put out some pie for the staff. The next year, some museum visitors noticed the pie and asked what was going on. And that’s how Pi Day was born.