Compound Interest

The math

Future Value = Principal × (1 + r/n)^(n × t)

Where r is the annual rate, n is compounding periods per year, and t is years.

A $10,000 deposit at 7% annual interest, compounded annually for 30 years:

• After 1 year: $10,700 (7% of $10,000 = $700 interest)
• After 2 years: $11,449 (7% of $10,700, not $10,000)
• After 30 years: $76,123 — almost 8x the original.

Simple interest at the same rate would have produced only $31,000 over 30 years (just $700/year, no compounding on prior interest).

The Rule of 72

A useful approximation: the time it takes for an investment to double is roughly 72 divided by the annual rate.

• At 6%, money doubles in ~12 years.
• At 8%, in 9 years.
• At 10%, in 7.2 years.

Useful for back-of-envelope thinking. A 25-year-old saving at 8% has roughly four "doublings" before retirement at 65 — meaning every dollar saved early can grow 16x in real terms. The same dollar saved at 50 has fewer doublings ahead and ends up much smaller.

Why starting early matters more than rate

A common but striking comparison:

• Investor A saves $5,000/year from age 25 to 35, then stops. Total contributions: $50,000.
• Investor B saves $5,000/year from age 35 to 65. Total contributions: $150,000.

At 8% annualized return, by age 65:

• Investor A has roughly $615,000 despite never adding after age 35.
• Investor B has roughly $566,000 after 30 years of contributions.

Investor A's contributions had more time to compound. The early decade is structurally worth more than three later decades.

Why credit-card debt destroys wealth

The same compounding works in reverse on debt. A $5,000 credit-card balance at 24% APR, if only minimum payments are made, can take 20+ years to pay off and end up costing several times the original balance in interest.

A 24% APR rate compounded daily produces an effective APY of about 27%. At that compounding rate, debts double in under three years if unpaid. This is why high-interest debt is treated as financial-priority #1 in personal-finance planning — paying down debt at 24% is mathematically equivalent to a guaranteed 24% return, which exceeds nearly all other available investments.

What investors should internalize

Three boring habits that compound interest makes powerful:

• Start now. Even small contributions become large over decades. Waiting for "more income" is the most common destroyer of long-run wealth.
• Don't interrupt the compounding. Selling investments to cover lifestyle inflation, taking 401(k) early withdrawals, or panic-selling in a bear market all reset the compounding clock.
• Reinvest, don't consume. Dividends and interest reinvested compound; cashed out, they don't. Most retirement accounts handle this automatically; taxable accounts often require conscious choice.

Where compounding shows up in DeFi

APY in DeFi is just compounding made transparent. A pool advertising 12% APY with daily compounding pays a slightly lower nominal rate that compounds to 12% effective. The same math applies, just at higher volatility and with the additional layer of smart-contract risk.

Auto-compounding vaults (Yearn, Beefy, Convex) automate the reinvestment of harvested rewards back into the strategy, capturing compound returns that would be lost in a manual claim-and-redeposit cycle. The economic effect is the same as compound interest in any traditional account; the implementation is just on-chain.