# Boo! Scaring up savings at Halloween

Photo courtesy of Pink Sherbet Photography

I’ve admitted it here before: I’m a dedicated DIYer. Pinterest is a huge playground for me, and I scout craft shows for ideas I can try at home. Like most Martha Stewart wanna bes, I leave a lot of projects undone. It can turn out to be an expensive past time.

After years of this back-and-forth, I’ve realized one important few thing: sometimes DIY is more expensive — in money and time. That’s why I included the following in my book, Math for Grownups. Yes, the example is based on my own, personal experience, except that the ending turned out differently. (The obscure character? Luna of Harry Potter fame.) Had I really thought it through before heading to Joann’s Fabric, I would have saved myself some cash and a lot of time.

Rita loves Halloweʼen, and she loves making her kidsʼ costumes. This year, her 10-year-old daughter has requested a velvet-like cape and gown so that she can dress as some obscure character from her favorite novel about magical kids.

The pattern Rita is using calls for 7 yards of fabric, 2 fancy fasteners, and 3 yards of fringe. Looking at the Sunday circular for the local fabric store, she sees that crushed panne velvet is on sale for \$2.99 per yard and the fringe is priced at \$4 per yard. Rita guesses that the fasteners are about \$5 each. To estimate her costs, she adds everything together:

(7 • \$2.99) + (3 • \$4) + (2 • \$5)

(In case you lost track, that’s 7 yards of fabric at \$2.99 per yard, 3 yards of fringe at \$4 per yard, and 2 frog clasps at \$5 each.)

\$20.93 + \$12 + \$10 = \$42.93

A terrifying price!

Rita is starting to think that a trip to a thrift shop might be a better investment of her time and money. Sometimes doing it yourself just isn’t worth it.

Do you have any scary costume stories? How have you learned to save money while DIY and celebrating Halloween?

Photo courtesy of N i c o l a

For the last week, I’ve been suffering from a terrible cold of some sort, which has now taken up residence in my chest. Sometimes I have my voice, sometimes I don’t. Sometimes I sleep, most of the time I don’t. Sometimes I have energy, most of the time I’m sprawled out on my sofa hoping that something watchable will show up on my television set. So, I’m taking the easy way out with a short post today.

Having gone back and forth between the drugstore many times in the last week, I can’t help but wonder how much this whole thing is costing me.

3 cans chicken soup: \$1.49 each = \$4.47

3 bags Riccola lemon/mint, sugar-free lozenges: \$2.05 = \$6.15

1 bottle ibuprofen, 80 count: \$7.99

1 bottle Delsym 12-hour cough syrup: \$11.79

TOTAL: \$30.40

At the grocery store today, I bought two bags of oranges for \$5. A good night’s sleep is free and so is tap water. Prevention is the cheapest medicine. Lesson learned.

I’ll be back on Friday with a real post — unless I continue to go downhill with this stuff. In the meantime, if you’d like to share your cost-cutting strategies for dealing with or avoiding the common cold, I’m all ears. It’s likely I’ll be reading it at 2:00 this morning, while in the midst of a coughing fit. (Yeah, you should feel sorry for me.)

Oh and if this isn’t enough of a math fix for you, yesterday was Ada Lovelace Day — honoring all of the women who are tops in STEM (science, technology, engineering and mathematics) fields. Share your favorite brainy chick at the Math for Grownups facebook page.

Photo courtesy of David Drexler

On Wednesday, I showed you how to calculate the amount of money you’ll need in retirement — based on a variety of variables, including your pre-retirement income, the percentage of that income that you can live on in retirement and the number of years you expect to be in retirement. I even suggested that you find three or four goals for this — low, middle and high amounts — so that you have some realistic flexibility.

Even better is monitoring this savings along the line. Knowing what you should have already stashed away at age 30 or 40 or 50 can help you stay on track. If you’re behind, you can ratchet up your savings. If you’re way ahead, you can plan to quit your career a little earlier (or just bask in the really soft cushion you’ve created). Keeping an eye on these benchmarks helps you create a better plan.

But these calculations will naturally include a variety of assumptions — from how much you’re putting away in savings to the interest rates or return on investments. There’s no good way to really predict these, but retirement ratios have gotten pretty good reviews from some financial experts.

Retirement Ratios

Charles Farrell (not the silent film star) of Northstar Investment Advisors created a set of multipliers, outlined in his book, Your Money Ratios, that make it really simple to estimate these benchmarks. (In this case, multipliers are merely numbers that you multiply by. In essence they’re parts of proportions.) Like my suggestion to have several goals, Farrell developed bronze, silver and gold standards. (Bronze is 70% of income, retiring at 70 years old; silver is 70% of income, retiring at 65 years old; and gold is 80% of income, retiring at 65 years old.) His website and book detail these standards and benchmarks in really handy tables.

Basically, Farrell offers multipliers for each standard and each age. Pull the multiplier from the table, multiply it by your salary and — viola! — you have easily calculated a good estimate for how much you should have already saved by that age and for that standard.

Let’s look a simple example: retiring at age 70, with 70% of your income. And let’s say you earn \$50,000 a year.  Here are four multipliers from Farrell’s tables: 30 years old at 0.45, 40 years old at 1.6, 50 years old at 3.5, 60 years old at 6.5 and 70 at 10.

30 years old: \$50,000 • 0.45 = \$22,500

40 years old: \$50,000 • 1.6 = \$80,000

50 years old: \$50,000 • 3.5 = \$175,000

60 years old: \$50,000 • 6.5 = \$325,000

70 years old: \$50,000 •10 = \$500,000

It’s not at all clear how Farrell came to these multipliers. (And I’m certain, like KFC’s secret recipe, he’s going to keep much of that to himself.) But, mathematically speaking, there’s something interesting to notice here. Your benchmarks are 10 years apart, but the difference between each goal is not a constant number. In other words, the difference between each consecutive year is not the same number.

Why is that? Well, if you think of the graph of compound interest, you’ll come to the answer quickly. Because compound interest is a curve, it increases quickly. This is a great thing when you’re dealing with savings. (It’s not so good with credit.) And if you look at the difference between each benchmark, you’ll see that over time, you’re retirement investments and savings are increasing by more and more.

And this should make perfect sense, if you look at the multipliers. These are not increasing in a constant way, either.

1.6 – 0.45 = 1.15

3.5 – 1.6 = 1.9

6.5 – 3.5 = 3

10 – 6.5 = 3.5

Each difference is slightly larger as you go up in age. If you were to graph the age and multiplier (or even product) on a coordinate plane (x-y axis), you’d have a curve.

The bottom line is this — as you age, you want your nest egg to increase exponentially, rather than linearly. In other words, you want your total to increase quickly, so that you can reach your retirement goals before you’re too old to take advantage of them.

What do you think of this process? How would having these benchmarks help you monitor your retirement savings more closely? Do you think it would be helpful to use these multipliers in your planning? Share your responses in the comments section.

# Real Savings Has Curves: The difference between simple and compound interest

Photo courtesy of Kevin Dooley

What’s the most common math question I get from grownups? Easy: What’s the big deal about compound interest? For some reason, this idea stumps some very smart people. But the whole thing is pretty simple really. (Ha!) It all comes down to one concept — curves vs. lines.

You probably know that simple interest is, well, simple. That’s because it’s linear. (Stay with me here. I promise it’s not too hard.) In other words, simple interest can be described as a line. Now in mathematics, lines are very specific things. They go on forever, for one thing. For another, they’re straight. So while I might casually use the word “line” to describe a squiggly while I’m doodling, that’s a huge no-no in math. Among the Pythagorii and Sir Isaac Newtons, there’s no such thing as a “straight line.” By definition, a line is straight, not curved.

Because simple interest is linear, it increases (and decreases) steadily. Remember graphing linear equations? Take a look:

Graph courtesy of MoneyTipCentral

The graph above is an example of simple interest. As time goes on (or as you look to the right on the “time” axis), the money, \$, increases. And it increases very steadily. If you can remember back to your algebra class, you know that each point on this line is found by taking the same steps — x number of “steps” to the right and y number of “steps” up. This is consistent. In other words, you don’t take 2 steps to the right and 1 step up and then 2 steps to the right and 4 steps down. (If you were really paying attention in algebra class, you might remember that this is a way of describing slope, which indicates the steepness of the line.)

Now curves are different. And, yep, you guessed it, compound interest is a curve. Here’s a general example:

Graph courtesy of MoneyTipCentral

If you looked at three points on this graph, you would find that the way to get from the first to the second to the third is not a consistent series of steps. There would be a pattern, yes, but it wouldn’t be the same each time. This is what we call a non-linear equation, because, well, it’s not linear. (Duh.)

But what can these graphs tell us? It’s not as hard as you might think. Take a look at the graphs themselves. As time increases, so does the money, right? (In other words, as you move to the right along “time” the graph moves up along “\$.”) But with the curve, the \$ gets bigger faster. It takes less time for the money to increase along the curve than it does along the line. (Follow me? If not, take a closer look at the graphs.)

That’s because of one simple fact: with compound interest, the interest is accrued on the principal (or original amount) and the interest. Each time the interest is calculated, the interest from the previous time period is added to the amount. On the other hand, with simple interest, the interest is accrued on the principal alone. That translates to a steady increase over time, rather than a sharp increase, like with the curve.

So what does this matter? Well, it depends on whether your spending or saving. Since with compound interest, the amount accrues faster over time, this is a good thing for savings or investments — but a bad thing for credit. And it’s the other way around for simple interest.

(Of course that is all moot, since unless you’re borrowing from good old dad, simple interest is pretty hard to come by.)

The point is this: if you can remember that simple interest is a line and compound interest is a curve, you will likely remember how simple and compound interest are figured — slow and steady or speedy quick.

Do you have questions about compound or simple interest? Is there another way that you remember the difference? Share your ideas in the comments section.

Photo courtesy of Criss!

It’s summer. It’s hot. I’m busy with 9 million things. And so today, I bring you an excerpt from my book, Math for Grownups. If you’re wondering how to figure out the best vacation deal for you, read through this example. A little bit of planning–and math!–can help you relax, while you’re saving some cash.

Going on vacation means packing, finding someone to take care of Fido, and taking some time off from work. It also means charging some pretty hefty items on your credit card.

The finances of vacationing can boggle the mind. And even with online trip planners and the ability to comparison-shop with the click of a mouse, planning a vacation can make you ready for another one.

Red and Emily are ready for their second honeymoon. After 25 years of marriage, two kids, and the stress of everyday life, they deserve it. So Red is going to surprise Emily on their anniversary with a 1-week getaway to Aruba.

For 5 years, he’s been secretly putting away a little cash here and there. He’s got \$7,500 saved up, and that’s just enough to whisk his bride away for some R & R. (That’s romance and rest.) Red has even arranged for Emily to take some time off from work.
But first he’s got to figure out how he can spend his vacation nest egg. After Emily goes to sleep, he cruises trip-planning websites looking for the best deal. And he’s very quickly overwhelmed.

There are all-inclusive packages, non-inclusive packages, romance packages, and adventure packages. Some include the cost of flights and drinks and meals. Others offer some combination of these features.

It’s going to be a long night.

Within an hour or so, Red has some options scribbled down on a piece of paper. He has chosen their destination—a secluded resort with 5-star dining, access to a private beach, a spa, and great online reviews. Now it’s on to the pricing. There are a number of options:

Because two of his options don’t include airfare, Red prices out some flights. He finds out that he can get two round-trip tickets for about \$925. Not bad!

If he chooses a non-inclusive option, he’ll need to pay for meals, drinks, and activities. And that requires more research. Red wonders whether there is a good way to estimate these.

He considers meals first. The resort includes a free breakfast, so he won’t need to include that in his calculations. But unless they’re going with the all-inclusive option, they will have to buy lunches and dinners. Red does some more research and comes up with the following numbers:

Average lunch → \$25/person
Average dinner → \$60/person
Average lunch → \$25/person
Average dinner → \$60/person

And because there are two of them, and they’ll be there for 7 full days:

Lunches: \$50 per day for 7 days = \$350
Dinners: \$120 per day for 7 days = \$840

It looks like the cost of meals will be \$350 + \$850, or \$1,190.

He and Emily aren’t big drinkers, so that’s pretty simple to figure out. Assuming that the cost of drinks is pretty high, he guesses \$25 a day for two fancy cocktails, and if they have a nice bottle of wine with dinner each night, that’ll run them about \$200 for the week.

(\$25 • 7) + \$200 = \$375

Now, Red thinks about activities. A day on a sailboat and some snorkeling sounds great (\$450). Then he’d like to book a few spa treatments for Emily (\$500).

\$450 + \$500 = \$950

Because all of the prices so far have included tax, Red doesn’t no need to do any math for that. But he will need to tip the baggage carriers, taxi drivers, servers, and spa staff. Red takes a shot in the dark, and guesses \$350 for all gratuities. (That could be too much, but it’s probably not going to be too little.)

This is a ton of information, and Red’s legal pad looks like a football coach’s playbook. He’d better get organized if he wants to book this trip and get some sleep. Red decides to make a list.

Package

All-inclusive = \$7,225

Romance package: \$6,150 (package) + \$925 (air) =  \$7,075

Hotel + Travel: \$4,340 (hotel/air) + \$1,915 (meals/drinks/tips) + \$950 (activities) =       \$7,205

A la carte: \$3,450 (hotel) + \$925 (air) + \$1,915 (meals, etc.) + \$950 (activities) =  \$7,240

Now Red can really consider his options.

The most expensive choice is à la carte, but all of the totals are pretty darned close. If he goes by price alone, the clear winner is the Hotel + Travel package. But that requires him to handle everything on his own—and honestly, he’s ready for bed.

On the other hand, the Romance package is only \$70 more. And right now, that extra bit of cash seems worth it. Red pulls out his credit card and books their flights and vacation packages. Then he snuggles up next to Emily and savors his little surprise!

How have you found the best travel deals? Share your ideas in the comments section.