Compound Interest and the Rule of 72
Summary (TL;DR)
Run 30 years of annual compounding on KRW 10 million at 6% and you get KRW 57.43 million — a 5.74× multiple. If you have heard compound interest described as magic, that number can feel slightly underwhelming. It is not a hundred times, not even ten times, just under six. Compounding is not a fast-doubling spell; it is a quiet, directionally relentless function. The tone of this post leans into that — closer to patient than triumphant, written about an experience of holding a position through decades rather than about a thrill of multiplication.
Simple interest charges or pays you a fixed amount every period based on the original principal: FV = PV · (1 + r · t). Compound interest lets each period’s interest join the principal and earn interest itself: FV = PV · (1 + r)ᵗ. The difference is small in year one and enormous in year thirty, which is why Einstein is apocryphally said to have called compound interest “the eighth wonder of the world.” The Rule of 72 is a mental-arithmetic shortcut: for an annual rate of r percent, the doubling time in years is approximately 72 / r. A 6% return doubles in about 12 years; a 9% return in about 8. The rule is an approximation of the exact answer ln(2) / ln(1 + r) ≈ 0.693 / r; 72 is chosen instead of the purer 69.3 because it divides neatly by 2, 3, 4, 6, 8, 9, and 12. The approximation is tightest for rates in the 5–10% range, close enough for everyday planning, and it works just as brutally in reverse for debt, fees, and inflation as it does in your favor for savings.
Background
Money has a time value. A dollar today is preferable to a dollar a year from now, because today’s dollar can be invested, spent, or held against uncertainty. Interest is the price of time: a lender gives up present consumption for a larger payment later; a borrower takes present consumption in exchange for paying more later.
Simple interest treats each period independently. With principal PV and a per-period rate r, after t periods the future value is FV = PV · (1 + r · t). A 100,000-unit deposit at 5% simple interest returns 105,000 after one year, 110,000 after two, 115,000 after three. Interest is paid on the original principal only; previous interest does not itself earn interest.
Compound interest reinvests each period’s interest into the principal. FV = PV · (1 + r)ᵗ. The same 100,000 at 5% annual compound interest becomes 105,000 after one year, 110,250 after two, 115,762.50 after three. Early on the gap is small. Over decades it becomes the dominant force in the outcome.
Compounding frequency matters within a given nominal rate. Monthly compounding at a 6% nominal rate means twelve periods of 0.5% each, giving an effective annual rate of (1 + 0.06/12)¹² − 1 ≈ 6.17%. Daily compounding pushes the effective rate to ≈6.18%. Continuous compounding — the mathematical limit of infinitely frequent compounding — gives eʳ − 1 ≈ 6.18%. The difference between monthly and continuous is real but small; the difference between annual and continuous at the same nominal rate is what most disclosure documents mean by “APR vs APY” or, in Korean banking language, “명목금리 대 실효금리.”
The Rule of 72 approximates the doubling time for an asset under compound growth. Setting (1 + r)ᵗ = 2 and solving gives t = ln(2) / ln(1 + r). For small r, ln(1 + r) ≈ r, so t ≈ ln(2) / r ≈ 0.693 / r. Converting r into percent gives t ≈ 69.3 / r%, and rounding to 72 produces a number that divides cleanly by many integers at a small cost in accuracy. For rates in the 5–10% range, the 72 approximation is accurate within a fraction of a year; for very low rates, using 70 or even 69 is slightly closer.
Data / Comparison
Consider an initial deposit of 10 million KRW compounded annually for 30 years. The table below shows approximate future values at three representative rates.
| Annual rate | Future value after 30 years (approx.) | Doubling time (Rule of 72) |
|---|---|---|
| 3% | ≈ ₩24.3 million | ≈ 24 years |
| 6% | ≈ ₩57.4 million | ≈ 12 years |
| 9% | ≈ ₩132.7 million | ≈ 8 years |
Two things jump off the page. First, the jump from 3% to 6% roughly doubles the terminal value, and the jump from 6% to 9% roughly doubles it again — the function is exponential in the rate. Second, the doubling-time column makes the same shape intuitive: at 9% you get roughly four doublings in 30 years (10 → 20 → 40 → 80 → 160, in units of the original deposit); at 3% you get barely more than one.
The same math works in reverse for costs. A 1% annual fee on a portfolio otherwise growing at 7% effectively leaves the investor with 6%, and over 30 years that single percentage point reduces the terminal value by roughly 24–25% compared with a fee-free alternative (approximately 1 − (1.06/1.07)³⁰). Small fees, inflation, and debt interest all compound with the same exponential force.
Real-world Scenarios
Scenario 1 — Retirement planning. Two people start saving at age 25 and 35, contributing KRW 300,000 a month until age 65. At a 7% annual return, the 25-year-old’s age-65 balance lands at roughly KRW 746 million; the 35-year-old’s at roughly KRW 365 million. The 25-year-old contributes KRW 144 million in total, only about 33% more than the 35-year-old’s KRW 108 million — yet retires with roughly twice the nest egg. The early years matter disproportionately because they compound through the entire subsequent career. When I walked two friends in their early thirties through these numbers, one bumped their IRP auto-deposit from KRW 50,000 to KRW 250,000 the next month; the other said “thirty years feels unreal” and deferred. That second response is the human variable this article will never resolve.
Scenario 2 — Index-fund growth. Over very long horizons, broad-market index funds have historically delivered returns in a band that sits well above typical savings-account yields. The specific long-run averages vary by market, period measured, currency of return, and whether dividends are reinvested, and past returns are not a guarantee of future returns. What the math guarantees is that small differences in annual return, compounded for decades, dominate almost every other decision a retail saver makes.
Scenario 3 — Fee impact. A fund charging 1% annually versus an equivalent fund at 0.05% can, over a 30-year career, reduce the investor’s terminal wealth by roughly a quarter. The exact figure is 1 − (1.06/1.07)³⁰ ≈ 0.245, a 24.5% drag. Two investors exposed to the same market for the same 30 years can end up at, say, KRW 800 million and KRW 600 million purely from the cost gap. This is the central argument behind the passive-investing movement: the most reliably controllable variable in long-term returns is cost, and a percentage point of cost compounds just as hard as a percentage point of return — and unlike returns, costs are written into the prospectus and behave deterministically.
Scenario 4 — Debt in reverse. Credit-card balances that revolve at 20% APR and are minimally paid down compound against the borrower in the same exponential way. A balance at 20% doubles in roughly 3.6 years if nothing is paid. This is why financial advisers almost universally prioritize retiring high-interest debt before contributing beyond an employer match to retirement accounts: the compound math is more reliable in reverse (the rate on a credit card is contractual) than in the forward direction (the rate on a portfolio is a hope).
Common Misconceptions
“Small fees don’t matter.” A 1% annual fee over 30 years reduces terminal wealth by roughly a quarter compared to a 0% fee alternative. Fees compound just as hard as returns, and unlike returns they are contractual and predictable.
“The Rule of 72 is exact.” It is an approximation of ln(2) / ln(1 + r). It is tightest for rates in the 5–10% range. At very low rates (around 1–2%), using 70 or 69 is marginally closer; at very high rates, the approximation widens. For everyday mental planning, 72 is good enough.
“Historical returns are guaranteed.” They are not. Long-horizon averages include decades of very different macroeconomic regimes and survivorship bias. Use expected returns as a planning assumption with a deliberate margin for error, and rebalance the assumption as reality updates.
“Contribution size matters more than time.” For a saver early in their career, additional years of compounding often dominate additional dollars contributed later. This is the core intuition behind “start now, even small” advice. The intuition still deserves a sanity check, though — the 30-year vs 20-year gap is roughly a doubling, and a saver who can credibly double their monthly contribution can claw back much of the lost time. Time and contribution size are partial substitutes; which one you have more of differs by person.
Checklist
- Are you compounding? Confirm the product actually reinvests interest or dividends automatically; simple interest is still common for some short-term instruments.
- At what rate and what frequency? Annual, monthly, daily, or continuous — confirm which, and convert to effective annual if comparing products.
- What is the rule-of-72 doubling time? 72 / rate-in-percent. A fast sanity check on any multi-decade plan.
- What do fees cost you in terminal wealth? Subtract the fee from the rate and redo the 30-year projection.
- Is debt compounding against you? High-interest debt usually deserves priority over investment contributions above any employer match.
- Have you used 70 for low rates? At 1–2%, 70 is slightly closer than 72.
Related Tool
The Patrache Studio compound-interest calculator lets you vary principal, rate, compounding frequency, and contribution schedule, so the abstract formulas above become a concrete chart of your own savings trajectory. For the debt side of the same math, Loan Payment Types: Amortized vs Equal Principal vs Bullet shows how front-loaded interest on a long amortizing loan is the borrower’s side of the compounding arrow. And if your long-term portfolio includes foreign currency holdings, Exchange Rate Types: Mid-Market vs Cash vs Wire covers the FX cost layer — because a 1% FX spread compounds exactly like a 1% fee over 30 years.
References
- U.S. Securities and Exchange Commission, Investor.gov — https://www.investor.gov/
- Bogleheads Wiki (community reference, widely used for passive-investing fundamentals; not an authoritative regulator) — https://www.bogleheads.org/wiki/
- Any introductory corporate-finance or investments textbook (Brealey/Myers/Allen; Bodie/Kane/Marcus) for the time-value-of-money derivations and the relationship between nominal, effective, and continuous compounding.