Compound Interest
Interest on interest makes money grow exponentially.
About this topic
Compound interest pays interest on both the original principal and the interest already earned. The formula A = P(1 + r/n)ⁿᵗ gives the final amount for principal P, annual rate r, n compoundings per year and t years. More frequent compounding gives slightly more money.
Compare 1000 dollars at 6% for 10 years. Compounded yearly it becomes 1000(1.06)¹⁰, about 1790.85. Compounded monthly it is 1000(1 + 0.005)¹²⁰, about 1819.40. Simple interest would give only 1600, showing the power of earning interest on interest. The rule of 72 says money doubles in roughly 72 divided by the percent rate years.
This is the core of savings accounts, retirement plans, student loans and credit cards. Starting to save early matters more than the amount, because time is the exponent. Debt grows the same way, which is why unpaid balances become so heavy.
Be sure to enter r as a decimal, divide the rate by n, and multiply the years by n. A common mistake is to use the annual rate for each period. Parentheses matter when using a calculator, so type the base first and then apply the exponent.
Key ideas
- A = P(1 + r/n)^(nt)
- More frequent compounding earns slightly more
- The Rule of 72 estimates doubling time
Quick check
Use cases: where Compound Interest helps
- Homework: review the key idea behind Compound Interest before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Compound Interest without notes.
- Visual learning: play with the interactive lab to see how Compound Interest changes when you adjust its inputs.
- Teaching a friend: explain Compound Interest in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Compound Interest?
Interest on interest makes money grow exponentially.
What will I learn in Compound Interest?
A = P(1 + r/n)^(nt). More frequent compounding earns slightly more. The Rule of 72 estimates doubling time.
Is Compound Interest part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Compound Interest lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Compound Interest?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.