The same machine in reverse
A savings balance grows by interest and then a deposit is added. A loan balance grows by interest and then a payment is taken away. One recurrence, one sign changed. Everything that made compounding powerful in Part 1 is what makes debt hard to escape here.
Guess before you read on
You owe $3,000 on a card charging 22% a year
You never spend another cent on it. Every month you pay the minimum the card asks for, which is 1% of what you owe plus that month's interest, with a floor of $25. How many years until the balance reaches zero?
Minimum payment rules differ between lenders. The one used here, a percentage of the balance plus the month's interest with a dollar floor, is one common structure and not a universal one. Your own card will state its rule in the agreement.
One recurrence, one sign changed
In Part 1, each month did two things: the balance grew by the interest rate, and then your deposit was added. Debt does the same two things. The balance grows by the interest rate, and then your payment is taken away.
One subtraction. That is the entire difference between the two machines. So a loan curves the same way savings do, and everything you worked out in Part 1 carries straight over with nothing changed.
One consequence matters more than the rest. Interest is charged on what you owe right now, not on what you originally borrowed. Last month's interest is part of this month's balance, so it earns interest of its own. That is compounding, working against you.
Run a debt
Try the card from the guess above. Then switch to a fixed payment and find the smallest one that clears it inside two years.
Set a fixed payment just below the threshold figure and the answer becomes Never. That is not a rounding artifact, it is the actual behavior of the debt.
What the after-inflation shortcut was hiding
Every figure in Module 1 was stated after inflation. That was a deliberate shortcut: it meant one fewer lever to reason about, and it meant every answer was already in today's money. This is where it gets paid back.
A nominal rate is the number somebody quotes you. A real rate is what survives once prices have moved, and it answers the question you actually care about: can you buy more than you could before? To convert between them you divide. Most people subtract, which is close enough at low rates and gets worse the higher the rates climb.
Push both rates up together, to 12% and 8%, and watch the subtraction shortcut drift away from the real answer.
Seven problems
Estimate first, then check. An estimate within 25% counts.
Four situations you have not seen
Different setups from the ones above. Two of them turn on knowing which numbers can legitimately be compared with which.
Write it down
Answers stay on this device. Nothing is graded and nothing is sent anywhere.
1. A debt you know about
Name a debt you or someone close to you holds. Work out one month's interest on it: the rate divided by twelve, times the balance. What does that number tell you that the monthly payment did not?
2. What the minimum changes
You now know what paying the minimum costs in time and in money. Does that change how you would use a card? Write down something you would actually do. "I would be more careful" is an intention, and intentions are easy to write.
3. The limit that matters to you
Read the fourth worked answer below, which lists what these models leave out. Which of those limits would matter most in your own situation, and would it make the picture better or worse?
Check yourself
Answer each one before revealing ours. If you read our answer first you will agree with it, which tells you nothing.
1. Say why debt compounds
Explain, without using the word "compound", why a debt left alone grows faster and faster.
2. The payment that never finishes
How do you work out, for any debt, the monthly payment below which it never clears? Do it for $5,000 at 24%.
3. Nominal against real
Explain the difference in your own words, and say how you convert one into the other.
4. Break the model
Name something these debt calculators leave out that would change what you should actually do.
Save or hand in your answers
This writes out everything saved on this device for Module 2, both parts: your guesses, every problem you attempted with the answer beside it, and all your written answers.
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.