What Is Compound Interest?
Compound interest is interest calculated on a balance that can include interest credited in earlier periods. Over time, this can produce faster growth than a simple-interest model because the accumulated balance becomes part of the base for later periods.
Compound Interest Formula
P = starting principal, r = annual interest rate as a decimal, n = compounding periods per year, t = time in years, and A = final balance.
The interest earned over the period is A − P when there are no additional deposits or withdrawals.
Worked Example
Suppose you start with 5,000 at an annual rate of 6% compounded monthly for 3 years. Convert 6% to 0.06, use 12 compounding periods per year, and use 3 years in the formula. The resulting balance is higher than the starting 5,000 because interest is repeatedly added to the balance.
Why Compounding Frequency Matters
Monthly, quarterly, semi-annual and annual compounding can produce different balances when the stated annual rate and other assumptions are held constant. Always use the compounding frequency specified by the account, loan or scenario you are modelling.
What If You Add Money Regularly?
With monthly or annual contributions, the final balance includes both the original principal and the growth of contributions. The timing of each contribution matters because money deposited earlier has more time to compound.
Simple Interest vs Compound Interest
Simple interest uses the original principal as the base in the standard model. Compound interest allows previously credited interest to participate in later calculations. The difference generally becomes more noticeable as the rate, time horizon or compounding effect increases.
Common Mistakes
- Using 6 instead of 0.06 for a 6% rate.
- Using the wrong number of compounding periods.
- Mixing an annual rate with a monthly period without converting the rate.
- Assuming a constant return represents an actual investment outcome.
Important Limitations
Real accounts and investments can have fees, taxes, changing rates, contribution rules or losses. A constant-rate calculation is a mathematical scenario, not a guarantee of future returns.
Use the Tervilo Compound Interest Calculator
Use the Compound Interest Calculator to model a starting amount, contributions, compounding frequency and time, then compare alternative assumptions.