Compound Interest
Learn how compound interest grows your money faster by earning interest on interest.
Definition
The Compound Interest Formula
- = Final amount (principal + interest)
- = Principal (starting amount)
- = Annual interest rate (as a decimal)
- = Time (in years)
Finding Just the Interest
Why It Grows Faster
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Worked Examples
You invest 1000 dollars at 5% compound interest for 3 years. How much will you have?
Identify the values
, , → Values identified
Write the formula
→ Formula ready
Substitute values
→ Values substituted
Calculate the power
→
Multiply by principal
→
Answer: After 3 years, you will have 1157.63 dollars (earning 157.63 dollars in interest).
Common Mistakes
Forgetting to add 1 to the rate inside the parentheses
Why it's wrong: Writing instead of gives a tiny number, not growth.
Correct: Always use . The 1 represents keeping your original money!
Using simple interest formula for compound problems
Why it's wrong: Simple interest is . Compound interest uses exponents: .
Correct: Look for keywords: "compounded" means use the exponential formula.
Not converting percentage to decimal
Why it's wrong: Using instead of will give astronomical results.
Correct: Always divide percentage by 100:
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Practice Problems
15 problemsIn the compound interest formula , what does the exponent represent?
Why It Matters
- Savings accounts: Your money grows faster over time
- Retirement funds: Small contributions become large sums over decades
- Investments: The stock market uses compound returns
- Credit cards: Debt can grow quickly if you only pay minimums
- Student loans: Interest compounds, increasing what you owe
Real World Applications
Retirement Savings
Retirement accounts use compound interest to grow small contributions into large nest eggs over 30-40 years.
Example:
Investing 100 dollars monthly at 7% for 40 years can grow to over 260000 dollars!
You invest 2000 dollars in a retirement account earning 6% compound interest.
How much will you have after 20 years?
Step 1: Write the mathematical expression
Use the formula :
Credit Card Debt
Credit cards compound interest monthly. High rates can quickly multiply what you owe.
Example:
A 1000 dollar balance at 20% APR becomes about 1220 dollars after one year if unpaid.
You have 500 dollars in credit card debt at 18% annual interest, compounded yearly.
How much will you owe after 3 years if you make no payments?
Step 1: Write the mathematical expression
Calculate the debt growth:
College Savings
529 plans and education savings accounts use compound interest to help families prepare for college costs.
Example:
Starting a 529 plan when your child is born gives 18 years of compound growth!
Key Takeaways
- 1Compound interest formula:
- 2Interest is calculated on principal PLUS previously earned interest
- 3Always add 1 to the rate: use , not just
- 4Convert percentage to decimal before calculating
- 5Compound interest grows faster than simple interest over time
- 6The longer the time, the bigger the difference becomes
Frequently Asked Questions
Glossary
- Compound Interest
- Interest calculated on the initial principal and all accumulated interest
- Principal
- The original amount of money invested or borrowed
- Exponential Growth
- Growth that increases at an ever-faster rate, like compound interest
- Compounding Period
- How often interest is calculated and added (annually, monthly, daily)
- Growth Factor
- The value that multiplies the principal to give final amount