Compounding and time
Module 1 showed that a dollar spent today costs more than a dollar, and that the gap widens the longer you would have held it. This part opens the mechanism up: where the growth comes from, why the line bends, and how long it takes before the growth is doing more work than you are.
First, three from last time
Before starting anything new. These come from Module 1, and the gap since you read it is doing the work here. Pulling something back out of your memory days later is what makes it stick, and it still works when you get the answer wrong.
Answer from memory. Do not look back until afterwards.
Now guess this one
You pay $200 a month into an account earning 5%
You never miss a month and you never take anything out. At some point the growth sitting in that account is worth more than every dollar you have paid into it. How many years does that take?
Where the growth comes from
A fixed rate of return does not produce a fixed amount of money. It produces a fixed percentage, and the thing it is a percentage of keeps getting larger.
Put $10,000 in at 5%. The first year it earns $500. That $500 joins the balance, so the second year takes 5% of $10,500 and earns $525. Twenty-five dollars is a small difference to start from, and it is the point. Growth joins the balance, and then it earns growth of its own.
Run that long enough and the yearly figure stops looking anything like $500. Watch for it in the chart below: the line bends upward instead of running straight. It also explains why buying something at 18 costs you so much more than buying the same thing at 45.
Watch the growth overtake you
The gray band is money you paid in. The green band above it is growth. The dashed line marks the point where the growth becomes worth more than everything you have contributed.
Drop the rate to 3% and the crossing stops happening at all inside forty years. Push the years out and you will find it, a long way past where 5% put it. The rate does not only change the size of the answer, it changes whether you live long enough to see the account start working harder than you do.
What a head start is worth
Module 1 measured this gap once, with fixed ages. Here you can move them. Two people pay in the same amount each month and stop at the same age. The only difference is when they started.
Set both stop ages far below the measuring age and something worth seeing happens: neither of them pays in for years, and the gap between them still widens.
Before moving on
Set the stop age to something early, like 30, and the measuring age to 65. Both people stop paying in decades before the end. Write down what that tells you about which years matter, and what you would change about your own plans because of it.
Seven problems
Estimate first, then check. Anything within 25% counts, because what you are practicing here is how to judge roughly how big a number should be.
Save or hand in your answers
This writes out your guess, every problem you attempted with the answer beside it, and anything you typed. It is a plain text file, so it opens on anything and attaches to anything.
Everything here is read out of this browser and written into a file on your own machine. Nothing is uploaded, because there is no server to upload it to. Clearing removes Module 2's answers only, and leaves Module 1 alone. If you are on a shared or school computer, use it when you are finished.