Compound Interest: The Math Behind Long-Term Wealth

Compound interest is the process of earning returns not just on your original principal, but also on the interest your principal has already earned. Over short time periods, the difference from simple interest looks minor. Over 20-30 years, it is the difference between modest and life-changing wealth.

How the Formula Works

The compound interest formula: A = P × (1 + r/n)^(n×t)

• A = final amount
• P = principal (starting amount)
• r = annual interest rate (as a decimal)
• n = times compounded per year
• t = years

Example: $50,000 invested at 7% annual return, compounded monthly, for 20 years becomes roughly $200,000. Without adding a single dollar more. The last five years of growth produce more absolute dollars than the first ten years combined.

The Rule of 72

Divide 72 by your annual interest rate and you get the approximate number of years it takes to double your money. At 6%, money doubles in 12 years. At 9%, it doubles in 8 years. At 12%, in 6 years.

This simple rule reveals why rate of return matters so much over long time horizons. A 3-percentage-point difference in annual returns does not feel dramatic year to year. Over 30 years, it can mean twice as much wealth.

What Interrupts Compounding

Three things break the compounding curve:

• Withdrawing principal early: Every dollar you pull out not only reduces your balance but also reduces the base that compounds going forward. The cost compounds too.
• High fees: A 1% annual fee sounds small. On a $500,000 portfolio over 30 years at 7% growth, a 1% fee costs roughly $200,000 in lost compounding. Fees matter enormously at scale.
• Timing the market: Missing the 10 best trading days in any 20-year period typically cuts returns by 50% or more. Consistent participation beats intermittent participation, even in down markets.