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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Before Summer Ends...
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Math That Matters
How to Negotiate Like a Woman -- and Win
Lilly Ledbetter, Equal Pay for Women, and Toyo Tires
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1. Who you gonna call? Bill Murray, the star of the Ghostbusters movie series, this week offered his picks for who should star in a reboot of the series, set to feature female-leads. Murray's picks: comedians Melissa McCarthy and Kristen Wiig, and actress Emma Stone. Said Murray, "There are some funny girls out there." Indeed there are. Maybe it was a coincidence, but we read about the reinvention of Ghostbusters the same week The New York Times and others that female representation of women in movies is, in fact, improving. Proof: Katniss Everdeen, the lead in The Hunger Games series, and played by Jennifer Lawrence: "Characters like Katniss Everdeen are changing girlhood and challenging tired stereotypes by not waiting for some guy to save the day: They're saving themselves and their worlds, too." Hear, hear.
2. Can we talk? Joan Rivers died this past week at the age of 81, and it may be easy to forget what a ground-breaking comedian she was. She joked about herself, her looks, her marriage and the conventions that seemed to suggest that a woman's only place was in the kitchen. Her daughter, Melissa, paid her a fitting tribute, reading a letter she wrote to her mom, who frequently stayed with her and her son. The letter is now posted online. Here's an excerpt. "Dear Mom: I received the note that you slipped under my bedroom door last night. I was very excited to read it, thinking that it would contain amazing, loving advice that you wanted to share with me. Imagine my surprise when I opened it and saw that it began with the salutation, “Dear Landlord...” I’m more than happy to have you use the house for social gatherings, but you cannot rent it out, advertise as “party central” or hand out T-shirts that say “F— Jimmy Buffett." We'll miss you Joan.
3. It's a watch -- that tells time! In case you somehow missed the biggest product announcement of the year, Apple, maker of devices that many covet, announced that it will release its first wearable device next year: a smart watch called the Apple Watch. There have been many, many stories touting the amazingness of this new thing, but we want to tip our hat to Ellen DeGeneres, who tweeted what a lot of us were thinking: "So excited for the Apple Watch. For centuries, we've checked the time by looking at our phones. Having it on our wrist? Genius."
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