Interest is money paid for the use of money, and it affects savings, loans, credit cards, and many everyday financial choices. If you save money in a bank account, interest can help your balance grow over time. If you borrow money, interest is the extra cost you pay back in addition to the amount you borrowed.
Understanding interest helps students compare choices and avoid expensive debt.
Key Facts
- Interest is the cost of borrowing money or the reward for saving money.
- Principal is the starting amount of money borrowed, saved, or invested.
- Simple interest formula: I = Prt, where I is interest, P is principal, r is annual rate as a decimal, and t is time in years.
- Total amount with simple interest: A = P + I = P(1 + rt).
- Compound interest formula: A = P(1 + r/n)^(nt), where n is the number of compounding periods per year.
- A higher interest rate, longer time, or more frequent compounding usually makes the total amount grow faster.
Vocabulary
- Interest
- Interest is the money paid for borrowing money or the money earned for saving or investing money.
- Principal
- Principal is the original amount of money saved, invested, or borrowed before interest is added.
- Interest Rate
- An interest rate is the percentage of the principal charged or earned over a specific time period.
- Simple Interest
- Simple interest is interest calculated only on the original principal.
- Compound Interest
- Compound interest is interest calculated on both the principal and previously earned interest.
Common Mistakes to Avoid
- Using 5 instead of 0.05 for a 5% interest rate is wrong because percent values must be converted to decimals in formulas.
- Forgetting to match the time unit to the rate is wrong because an annual rate needs time measured in years unless the rate is adjusted.
- Confusing interest with total amount is wrong because interest is only the extra money, while the total amount includes the principal plus interest.
- Assuming all loans cost the same is wrong because different rates, fees, repayment times, and compounding rules can greatly change the total cost.
Practice Questions
- 1 Mia saves $200 in an account that earns 4% simple interest per year. How much interest will she earn after 3 years, and what will her total balance be?
- 2 A student borrows $500 at 6% simple interest per year for 2 years. How much interest will they owe, and what total amount must be repaid?
- 3 Two savings accounts both start with $100. Account A has a higher interest rate, but Account B compounds interest more often. Explain why the better choice depends on the exact rate, compounding schedule, and time kept in the account.