Compound Interest

⚠️ DISCLAIMER: I am not a financial advisor. This is not financial advice. These are notes on a system. Do your own research.

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 applies to the principal), compound interest creates exponential growth over time.

Albert Einstein allegedly called it “the eighth wonder of the world” — though there’s no evidence he actually said this. What is true: compound interest is the primary mechanism by which wealth grows and the primary reason early investing matters more than late investing with more money.

The Formula

The compound interest formula is:

A = P(1 + r/n)^(nt)

Where:

A = Final amount
P = Principal (initial investment)
r = Annual interest rate (decimal)
n = Number of times interest compounds per year
t = Time in years

Example: $10,000 at 7% for 30 years

Inputs:

P = $10,000
r = 0.07 (7%)
n = 12 (monthly compounding)
t = 30 years

Calculation: A = 10,000 × (1 + 0.07/12)^(12×30) A = 10,000 × (1.00583)^360 A = 10,000 × 8.116 A = $81,165

Your $10,000 became $81,165 — an 8x return — just by sitting there.

Why Time Matters More Than Amount

The most counterintuitive aspect of compound interest is that when you invest matters more than how much you invest.

Scenario	Monthly Investment	Years	Total Invested	Final Value (7%)
Early Start	$200/mo	40 years (age 25-65)	$96,000	$525,000
Late Start	$400/mo	20 years (age 45-65)	$96,000	$208,000
Very Late	$800/mo	10 years (age 55-65)	$96,000	$138,000

All three people invested the same total amount ($96,000). The early starter ends up with 4x more money — not from being smarter or luckier, but from starting earlier.

This is why the standard advice is: start now, with whatever you have.

The Rule of 72

A quick mental math shortcut: divide 72 by your interest rate to estimate how many years it takes to double your money.

Interest Rate	Years to Double
4%	18 years
6%	12 years
7%	~10 years
10%	7.2 years
12%	6 years

At 7% (roughly the historical stock market average after inflation), your money doubles every ~10 years.

Compound Interest Works Both Ways

Here’s the uncomfortable truth: debt compounds too.

Credit card debt at 24% APR doubles in 3 years. That $5,000 balance you’re “paying minimum on” becomes $10,000, then $20,000. The same mathematical force that builds wealth destroys it when you’re on the wrong side.

The Dark Side: Credit Card Math

Scenario: $5,000 credit card balance at 24% APR, paying only minimum payments (2% of balance or $25, whichever is higher)

Result:

Time to pay off: 28 years
Total interest paid: $12,400
Total paid: $17,400 for a $5,000 purchase

This is why credit card companies are very profitable.

Practical Applications

1. Start Your Emergency Fund Now

Even small amounts compound. $50/month at 4% (high-yield savings) for 5 years = $3,316. Not life-changing, but a real emergency fund that started from almost nothing.

2. Maximize Tax-Advantaged Accounts

Compound interest is more powerful when you’re not losing 20-30% to taxes every year. See Tax-Advantaged Accounts for details.

3. Automate and Forget

The best investment strategy is one you don’t think about. Set up automatic contributions and let compound interest do its job over decades.

4. Pay Off High-Interest Debt First

If your debt interest rate exceeds your expected investment return, you’re mathematically better off paying down debt. A guaranteed 24% return (avoiding credit card interest) beats an uncertain 7% market return.

Common Misconceptions

'I'll start investing when I make more money'

This is backwards. The earlier you start, the less total money you need to invest. Someone who invests $100/month from age 22-32 (10 years) and then stops will often have more at 65 than someone who invests $100/month from age 32-65 (33 years). Time beats amount.

'The stock market is too risky'

Over any 30-year period in US history, the stock market has had positive returns. The “risk” is in short-term volatility. If your time horizon is decades, compound interest in diversified index funds has historically been the most reliable wealth-building tool available to regular people.

'I need to pick the right stocks'

No. Index funds that track the entire market (like total stock market funds) let you capture the average return without trying to be clever. The average return, compounded over decades, is enough. Most professional fund managers fail to beat the index anyway.

The Bottom Line

Compound interest is:

The reason to start investing now, even with small amounts
The reason debt is dangerous, especially high-interest debt
The reason time is the most valuable investing resource
The mathematical engine behind long-term wealth building

You don’t need to be clever. You need to be early, consistent, and patient.

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