What is Compound Interest?
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest (which only calculates interest on the original principal), compound interest earns interest on interest — creating an exponential growth curve rather than a linear one.
The effect is modest in the short term and extraordinary over long periods. A $10,000 investment earning 8% simple interest grows by $800 each year — a straight line. The same investment with 8% compound interest grows by $800 in year 1, $864 in year 2, $933 in year 3, and accelerates from there. After 30 years, simple interest yields $34,000 while compound interest grows the same principal to $100,627.
This is why starting to invest early — even small amounts — is so powerful. Time is the amplifier of compounding. A 25-year-old who invests $5,000 and earns 8% annually will have $50,313 at age 55 without ever investing another dollar. The same $5,000 invested at age 45 grows to only $10,795 by age 55.
The Compound Interest Formula
The formula for compound interest with periodic compounding is:
A = P × (1 + r/n)^(n×t)
Compounding Frequency: Does It Matter?
The frequency of compounding affects the final amount, but the difference between monthly and daily compounding is smaller than most people expect:
For $10,000 at 8% for 10 years:
• Annual compounding: $21,589
• Quarterly compounding: $22,080
• Monthly compounding: $22,196
• Daily compounding: $22,253
The difference between annual and daily compounding is about $664 on a $10,000 investment over 10 years. While meaningful, it is far less impactful than the interest rate itself or the length of the investment period.
The type of account matters more than the compounding frequency. High-yield savings accounts compounded daily at 5% will outperform a traditional savings account compounded monthly at 0.5% by an enormous margin.
The Rule of 72
The Rule of 72 is a quick mental math shortcut to estimate how long it takes money to double at a given interest rate:
Divide 72 by the annual interest rate to get the approximate doubling time in years.
• At 6% annual return: 72 ÷ 6 = 12 years to double
• At 8% annual return: 72 ÷ 8 = 9 years to double
• At 10% annual return: 72 ÷ 10 = 7.2 years to double
• At 12% annual return: 72 ÷ 12 = 6 years to double
This rule works in reverse too — if you want your money to double in 6 years, you need an interest rate of approximately 72 ÷ 6 = 12%.