Compound interest vs. simple interest
Simple interest is calculated only on the original principal for the entire period: interest = principal × rate × time. The amount of interest earned each period stays the same.
Compound interest is calculated on the principal plus any interest already accumulated. Because each period's interest gets added to the balance that future interest is calculated on, the amount earned grows larger each period — this is often summarized as 'interest earning interest.'
The compound interest formula
The standard formula is: A = P × (1 + r/n)^(n×t), where A is the final amount, P is the principal, r is the annual interest rate as a decimal, n is the number of times interest compounds per year, and t is the number of years.
The total interest earned is simply A minus P. Increasing any of the four inputs — principal, rate, compounding frequency, or time — increases the final amount, but time and compounding frequency matter more than they might first appear, because their effect is exponential rather than linear.
Why compounding frequency matters
The same annual rate produces a different result depending on how often it compounds. Interest that compounds monthly (n = 12) grows a balance faster than interest that compounds annually (n = 1), because interest starts earning its own interest sooner.
The difference between annual and monthly compounding is usually modest at low rates over short periods, but becomes more noticeable at higher rates or over longer time horizons, since each small gain compounds on top of the last.
Why starting early matters most
Because compounding is exponential, time in the market tends to matter more than the exact rate of return, especially for long-term goals like retirement savings. A balance given an extra decade to compound can end up substantially larger than one that starts a decade later, even at the same rate — the earlier money has more periods to earn interest on its own interest.
This is also why compound interest works against borrowers on debt that compounds, such as credit card balances: unpaid interest gets added to the balance, and future interest is then charged on that larger amount too, which is part of why revolving debt can grow quickly if only minimum payments are made.
Frequently asked questions
Is compound interest always better than simple interest?
For a saver or investor, yes — compounding grows a balance faster. For a borrower, compound interest on unpaid balances works in the opposite direction, increasing the amount owed faster than simple interest would.
Does more frequent compounding always make a big difference?
It helps, but the effect is smaller than the effect of the interest rate itself or the length of time invested. Frequency matters most at higher rates over longer periods.
What's the difference between interest rate and annual percentage yield (APY)?
The stated interest rate is the nominal annual rate before compounding is applied. APY reflects the actual annual return after accounting for compounding frequency, so APY is typically slightly higher than the nominal rate when compounding happens more than once a year.
How do regular contributions affect compound growth?
Adding money regularly on top of compounding growth accelerates the balance further, since each new contribution also has time to compound. This combination of regular contributions plus compounding is the basis of most long-term savings and retirement strategies.