Read the notes, then try the practice. It adapts as you go.When you're ready.
Session Length
~13 min
Adaptive Checks
12 questions
Transfer Probes
7
Compound interest is one of the most powerful concepts in finance, often called the eighth wonder of the world. Unlike simple interest, which is calculated only on the original principal, compound interest calculates interest on both the principal and all previously accumulated interest. This creates exponential growth over time, meaning money grows faster and faster the longer it is invested. Understanding compound interest is essential for making informed decisions about savings, investments, loans, and credit cards.
The compound interest formula A = P(1 + r/n)^(nt) captures how four variables interact: the principal amount (P), the annual interest rate (r), the compounding frequency (n), and time (t). Small changes in any of these variables can produce dramatically different outcomes over long periods. The Rule of 72 provides a quick mental shortcut for estimating how long it takes money to double at a given rate. Comparing APR (the stated rate) to APY (the effective rate after compounding) reveals how compounding frequency affects the true cost of borrowing or the true return on savings.
Mastering compound interest empowers students to make better financial decisions throughout their lives. From choosing between savings accounts to understanding why credit card debt can spiral out of control, from planning for retirement decades in advance to evaluating investment opportunities, compound interest is the mathematical engine behind wealth building and debt accumulation alike.
One step at a time.
Interest calculated on both the initial principal and all previously accumulated interest, causing exponential growth over time.
Example: A $1,000 deposit earning 5% annually becomes $1,050 after year one, then $1,102.50 after year two because interest is earned on $1,050, not just $1,000.
How often interest is calculated and added to the principal within a given period. More frequent compounding yields higher effective returns.
Example: A 12% annual rate compounded monthly applies 1% each month, yielding more than 12% annually because each month's interest earns interest in subsequent months.
APR (Annual Percentage Rate) is the stated yearly rate without compounding effects; APY (Annual Percentage Yield) reflects the actual return after compounding is factored in.
Example: A credit card with 24% APR compounded monthly has an APY of about 26.82%, meaning you actually owe more than the stated rate suggests.
The principle that a dollar today is worth more than a dollar in the future because of its potential to earn compound interest over time.
Example: Receiving $10,000 today and investing it at 7% compounded annually is worth about $19,672 in 10 years, making the present dollar far more valuable.
A quick estimation method where dividing 72 by the annual interest rate approximates the number of years needed to double an investment.
Example: At a 6% annual return, an investment roughly doubles in 72 / 6 = 12 years. At 9%, it doubles in about 8 years.
The initial amount of money deposited or borrowed before any interest is applied. In compound interest calculations, the principal serves as the starting base upon which all future interest is calculated. A larger principal produces proportionally larger interest amounts each period.
Example: If you deposit 5,000 dollars into a savings account, that 5,000 is your principal. All future interest calculations start from this base amount.
Interest calculated only on the original principal amount, without including any previously earned interest. Simple interest grows linearly over time, in contrast to compound interest which grows exponentially. The formula is I = P times r times t.
Example: A 1,000 dollar loan at 5 percent simple interest for 3 years costs 150 dollars in total interest (1,000 times 0.05 times 3), regardless of how interest is paid.
The theoretical limit of compounding frequency where interest is calculated and added to the principal continuously, every infinitesimal moment. The formula uses Euler number e: A = Pe^(rt). While no real bank compounds truly continuously, it represents the mathematical ceiling of compounding benefits.
Example: One thousand dollars at 10 percent continuously compounded for 1 year becomes 1,000 times e^0.10 = 1,105.17 dollars, slightly more than daily compounding would produce.
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