Compound Interest Cheat Sheet

The core ideas of Compound Interest distilled into a single, scannable reference — perfect for review or quick lookup.

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Quick Reference

Compound Interest

Interest calculated on both the initial principal and all previously accumulated interest, causing exponential growth over time.

Compounding Frequency

How often interest is calculated and added to the principal within a given period. More frequent compounding yields higher effective returns.

APR vs APY

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.

Time Value of Money

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.

Rule of 72

A quick estimation method where dividing 72 by the annual interest rate approximates the number of years needed to double an investment.

Principal

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.

Simple Interest

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.

Continuous Compounding

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.

Key Terms at a Glance

Compound Interest:Interest calculated on both the initial principal and all previously accumulated interest, resulting in exponential growth.

Simple Interest:Interest calculated only on the original principal amount, producing linear growth over time. Formula: I = P x r x t.

Principal:The initial amount of money deposited, invested, or borrowed before any interest is applied.

APR (Annual Percentage Rate):The stated yearly interest rate without accounting for the effect of compounding.

APY (Annual Percentage Yield):The effective annual return after accounting for compounding frequency. Always equal to or greater than APR.

Compounding Frequency:How often interest is calculated and added to the principal (annually, quarterly, monthly, daily, or continuously).

Rule of 72:A quick estimation method: divide 72 by the annual interest rate to approximate how many years it takes to double an investment.

Time Value of Money:The principle that money available now is worth more than the same amount in the future due to its potential earning capacity.

Continuous Compounding:The theoretical limit of compounding frequency, using the formula A = Pe^(rt) where e is Euler number (approximately 2.71828).

Future Value:The value of a current asset at a specified date in the future based on an assumed rate of growth through compound interest.

Present Value:The current worth of a future sum of money, discounted at a specific rate to account for the time value of money.

Real Interest Rate:The nominal interest rate adjusted for inflation, reflecting the true change in purchasing power.

Annuity:A series of equal payments made at regular intervals. The future value of an annuity accounts for compound interest on each payment.

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