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← Money, Drawn

Money, Drawn

Four everyday money ideas, each drawn as a strip of paper: a paycheck's parts, a tax bracket as a cut bar, interest as last year's bar plus a slice, and a loan's shrinking interest.

Spark & Whetstone · sparkwhetstone.org/learn/money-drawn · CC BY-NC-SA 4.0. Answers are at the end, so you can try each question first.

Lesson 1. A paycheck in parts

The number on a job offer is not the number that reaches the bank. Draw the gross pay as one long bar, then cut off each piece that leaves before you see it: tax, a retirement saving, health cover.

The piece that is left is take-home pay. Seeing the pieces as lengths makes it easier to talk about them: which ones you choose, which ones you do not, and which ones change when pay changes.

Question. A paycheck is $2,000 before anything comes out. $300 goes to tax, $100 to retirement and $150 to health cover. What reaches the bank?

  1. $1,450
  2. $1,700
  3. $1,550

Say it back. In your own words: why is the take-home bar shorter than the pay on the offer?

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Lesson 2. A bracket is a cut bar

Here is a made-up tax system, simpler than any real one: the first $10,000 you earn is taxed at 10%, and every dollar above $10,000 is taxed at 20%.

Draw your income as a bar and cut it at $10,000. The left piece pays 10% and the right piece pays 20%. On $15,000 that is $1,000 on the first piece and $1,000 on the second: $2,000 in all.

A common worry is that a raise into a higher bracket makes all your pay taxed at the higher rate. The bar shows why it cannot: the cut is fixed, and only the dollars to the right of it pay the higher rate.

Question. In the made-up system, a raise takes you over the $10,000 line. What happens to the tax on your first $10,000?

  1. It stays at 10%; only the dollars above the line pay 20%.
  2. It goes up to 20%, the same as the new dollars.
  3. It disappears once you cross the line.

Say it back. Say it back: why can a raise never leave you with less after tax in a bracket system like this one?

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Lesson 3. Interest is a slice

Savings interest of 5% a year means each year the bar grows by a slice that is 5% of how long it already is.

Start with $1,000. After a year the slice is $50, so the bar is $1,050. Next year the slice is 5% of $1,050, which is $52.50, so the bar is $1,102.50.

The slice grows because the bar it is cut from grows. That is all compounding is: this year's bar is last year's bar plus a slice of itself.

Question. You save $1,000 at 5% a year, added once a year. How much is there after two years?

  1. $1,102.50
  2. $1,100.00
  3. $1,105.00

Say it back. In your own words: why is the second year's interest bigger than the first?

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Lesson 4. A loan's shrinking slice

A loan works the same way in reverse. Each month the lender cuts an interest slice from what you still owe, and your payment covers that slice first. Whatever is left of the payment shortens the bar.

Early on the bar is long, so the interest slice is big and most of the payment goes to it. As the bar shrinks, the slice shrinks, and more of the same payment goes to the loan itself.

That is why paying a little extra early on shortens a loan so much: every extra dollar shortens the bar the next slice is cut from.

Question. You owe $10,000. Interest is 6% a year, charged as 0.5% each month. What is the first month's interest slice?

  1. $50
  2. $600
  3. $500

Say it back. Say it back: why does more of each payment go to the loan itself as time goes on?

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At the table: Paper paychecks

Players: 2 to 6, a teenager welcome. You'll need: strips of paper, scissors, a pencil.

  1. Each person cuts a strip and writes a pretend monthly pay on it.
  2. Take turns naming one thing that comes out (tax, rent, savings) and cutting that piece off, with a rough length that matches.
  3. Lay the leftover strips side by side. Talk about one piece you would choose to make longer and one you cannot change.

Answers

  1. $1,450 — The three pieces are $300 + $100 + $150 = $550. The rest of the bar is $2,000 − $550.
  2. It stays at 10%; only the dollars above the line pay 20%. — The raise only lengthens the right-hand piece. The left piece, and the 10% on it, are exactly as they were.
  3. $1,102.50 — Year one adds $50, making $1,050. Year two adds 5% of $1,050, which is $52.50.
  4. $50 — One per cent of $10,000 is $100, and half of that is $50. Next month the slice is a little smaller, because you owe a little less.