Why your choices matter
Most people judge a purchase by its price. That leaves out the larger number: what the money would have become if it had stayed invested. This part is about seeing both, and then practicing until you can estimate it without a calculator.
Before you read anything, guess
You spend $500 today instead of investing it
Assume that money would have earned 5% a year after inflation, compounded monthly, and you leave it alone for 20 years. Write down what you think it would have been worth. Do not calculate. Guess.
Guessing first is what makes this work. Read the answer straight away and it will feel like you have learned something, when mostly you have just recognized it.
What opportunity cost actually means
Opportunity cost is the future you gave up to have the thing you bought. When you spend money you lose more than the price on the tag. You also lose everything that money would have grown into if you had left it alone.
Take that $500 laptop. The price is $500. But invested at 5% for 20 years it would be …. So the choice did not cost you $500. It cost you …, because that is what you gave up to have the laptop: the $500 itself plus … of growth that never happened.
Do not add those two pieces together. They are one number shown in two parts. The whole ending balance is the cost, because spending the money leaves you holding nothing where that balance would have been.
Why small repeated choices matter more than large single ones
You can absorb one $500 decision. A $500 habit every month is a different size of problem. Over 20 years at the same 5%, $500 a month adds up to … of spending, and it costs you …, because the earliest payments have almost the full 20 years to grow. The growth you give up, …, comes to more than everything you actually spent.
Work out your own number
Pick a real decision. A phone, a car, a subscription, a trip, or a monthly habit. Put it in and see what it costs across the horizon you choose.
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Five worked examples
Select any row to load it into the calculator above. These figures are produced by the same model the calculator uses, at the moment you load this page, so they cannot fall out of step with it.
| Choice | You spend | It costs you | Growth given up | Per dollar |
|---|
Notice what changes between rows one and two. Same $500, same rate. The only difference is how long the money had to work. Twenty-seven extra years roughly quadruples the cost.
How to estimate this without a calculator
Growth is hard to do in your head because multiplying by 1.05 nineteen times is hard to do in your head. Doubling is easy. So the trick is to stop thinking about the rate and start counting doublings.
Step one: how long is one doubling?
Divide 72 by the interest rate. That is roughly how many years the money takes to double. At the 5% this module uses, 72 divided by 5 is 14.4, so money doubles about every 14 years. The table below keeps the .4, which is why the years in it climb by a little more than 14 each time.
Why 72 and not some other number: it is the one that happens to work across the range of rates people actually deal with. There is real mathematics behind it, and you do not need it to use the rule.
Step two: how many doublings fit?
Divide the number of years by the length of one doubling, then double your starting amount that many times.
| Doublings | Years, at 5% | $500 becomes |
|---|---|---|
| 1 | about 14 | $1,000 |
| 2 | about 29 | $2,000 |
| 3 | about 43 | $4,000 |
| 4 | about 58 | $8,000 |
Most questions will not land on a whole doubling, and that is the part worth practicing. Twenty years at 5% is 20 divided by 14, so a bit under one and a half doublings. One doubling takes $500 to $1,000, and you are not quite halfway to the next, so call it somewhere around $1,300. The calculator on this page says $1,356. That is close enough to catch a wrong answer, which is the entire job.
This also explains the line under the table above. Twenty-seven extra years is close to two doublings, and two doublings is four times as much. That is where "roughly quadruples" comes from, and once you can count doublings you can see it without being told.
The rule assumes the rate holds steady the whole time, which no real return does. Module 3 is about what changes when the rate is an average rather than a promise.
Seven problems
Estimate first, then check. Count doublings, using the method above. Do not reach for the calculator. Anything within 25% counts as correct here, because what you are practicing is how to judge roughly how big a number should be. A calculator can do the exact part for you. It cannot tell you when its answer looks wrong.
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