Interest Compounds Both Ways

The story: Same math, two directions

Alex holds a savings jar and Jade holds a credit card while two meters show Jade’s debt growing faster than Alex’s savings.

1. Narrator: Alex has $500 in savings. Jade owes $500 on a credit card. Both balances grow with interest, in opposite directions.
2. Alex: My savings earns interest, so the bank adds a little to my balance every month.
3. Jade: My card charges interest, and the rate is a lot higher than what Alex earns.
4. Narrator: Next month, interest is figured on the new, bigger balance. Interest on interest is called compound interest.
5. Narrator: Over the years, Alex’s savings grow slowly. If Jade pays nothing, the debt grows faster, because the rate is higher.
6. Jade: So the same math that helps a saver works against a borrower.
7. Narrator: Interest compounds both ways, and time makes either side bigger.

What you’ll learn

1. Interest is a price

   Interest is the price of using someone else’s money. When you save at a bank, the bank pays you interest. When you borrow, you pay the lender interest. The rate is that price, shown as a percent per year.

2. Simple vs compound

   Simple interest is paid only on the principal, the starting amount. Compound interest is also paid on interest already added. Each period the base gets bigger, so the growth speeds up.

   Example: $500 at 10% a year compounds to $550 after one year, then $605 after two years. Simple interest would stop at $600.

3. Borrowers usually pay more

   Lenders charge borrowers a higher rate than banks pay savers. The gap is how lenders cover costs and earn money. So the same dollar usually grows faster as debt than as savings.

4. Time is the multiplier

   The longer money sits, the more compounding adds up. That helps a saver who starts early, and it hurts a borrower who carries a balance for years.

Key words

interest

the price of using someone else’s money

principal

the starting amount saved or borrowed

compound interest

interest paid on the starting amount and on past interest

rate

the price of money, shown as a percent per year

Common questions

What’s the difference between APR and APY?

Both describe yearly rates. APR is used for loans and cards. APY is used for savings and counts compounding. Later lessons on borrowing and savings cover each one.

Remember this

Make interest work for you, not against you.

Try it: Run the numbers on compounding

1. Use the sample: $500 at an example 5% a year for 10 years, or your own numbers.
2. Run it in the Investor.gov compound interest calculator.
3. Change the rate to a card-like 20% and compare the two results.

Run the sample numbers, or your own, in the Investor.gov compound interest calculator.