Money and taxes · Some practice · about 30 minutes
How Interest Works
Interest is the price of using money. When you save, a bank pays you interest; when you borrow, you pay it. Compound interest can grow your savings over time, and it can also make credit card debt grow if you carry a balance.
When to teach it: Watch from about 9, help from about 11, do it alone from about 14.
You'll need
- A calculator with an exponent key (^ or x^y)
- Paper and pencil
- A savings account disclosure or a credit card statement, if you have one
Step by step
Tick each step as you go if you like; ticks stay on this device.
Math
How it works: The compound interest formula
In A = P(1 + r/n)^(nt), P is the starting amount, r is the yearly rate as a decimal (5% = 0.05), n is how many times a year interest is added, t is the number of years, and A is the ending amount.
Worked example: you put $1,000 in savings at 5% a year, compounded monthly (n = 12), for 10 years. A = 1,000 × (1 + 0.05/12)^120 ≈ $1,647.01. With simple interest you'd have $1,000 + ($1,000 × 0.05 × 10) = $1,500. Compounding earned about $147 more. The APY for 5% compounded monthly is (1 + 0.05/12)^12 − 1 ≈ 5.12%.
Debt compounds too, working against you. Hypothetical card: a $1,000 balance at 24% APR (2% a month) and no new purchases. Paying $25 a month takes about 82 months, almost 7 years, and costs about $1,032 in interest. Paying $100 a month takes 12 months and costs about $127 in interest. Real cards usually use a daily rate, so actual numbers differ a little.
A = P(1 + r/n)^(nt)
Try it: Start with $100 at 5% a year. Year 1: $105. Year 2: $110.25. Keep going on a calculator for 10 years; you should get about $162.89. Then list simple interest ($5 a year) beside it and compare the two columns.
Keep learning: Ray's Arithmetic · Business Cases
Teaching it to your kids
- Pay a little 'family interest' on money your child leaves in a home savings jar for a month, so they see money earn money.
- Graph simple and compound growth side by side on graph paper and look for where the lines pull apart.
- Find the Minimum Payment Warning box on a real credit card statement together and read it out loud.
- The CFPB aims its lesson on minimum payments at ages 11 to 14, a good age to start this topic.
Tips
- Compare savings accounts by APY and credit offers by APR.
- Money left alone longer has more time to compound, so starting early matters.
- An account's plain interest rate doesn't include compounding; its APY does.
Common mistakes
| Mistake | Instead |
|---|---|
| Paying only the minimum on a credit card | Pay the full balance if you can, or as much over the minimum as you can. |
| Putting 5 instead of 0.05 into the formula | Change percents to decimals by dividing by 100. |
| Mixing up time units | Use the yearly rate for r, the number of times per year interest is added for n, and years for t. |
Where to get help
- If card debt is hard to manage, look on your credit card statement: it lists a toll-free number for credit counseling information.
Sources
Free how-to guides for families, with nothing to earn, pass or send in. They follow U.S. rules and sources; your owner's manual, product labels and state and local rules come first. This guide explains how things work; it isn't personal financial, tax or legal advice.