Entry № 15 · logged Oct 3, 2026Free, no sign-upCompound Interest · Investing

The Rule of 72: doubling time on the back of an envelope.

At 7% money doubles in about 72 / 7 = 10.3 years. The shortcut is famous because it is nearly right — the slip below posts the exact monthly-compounded doubling time beside it for any return you enter, plus the full growth ledger around it.

At 7%: shortcut says 10.3 years, exact monthly math says 9.9. Close enough to plan on, honest enough to check.

The growth ledger, Form CI-15. Post a starting balance and a monthly deposit; the slip compounds interest monthly, posts the year-by-year balance, and separates what you deposited from what growth added.

What you post Starting amount ($) Already saved or invested today. Zero is a fine start — the deposit does the early work. Monthly deposit ($/mo) Posted at the end of each month, after that month’s interest.

How it grows Annual return (%) A savings account might post 4%; a diversified portfolio has averaged near 7% after inflation-free math. Returns are never guaranteed. Years Inflation (%) Only drives the “today’s dollars” line — what the final balance buys in current terms.

Year	You posted	Interest posted	Balance

Math: each month the balance earns one-twelfth of the annual return, then your deposit posts. Steady returns are a modelling convenience — real markets wander year to year, and taxes and fees are not in this ledger.

How Compound Interest Worksinterest on interest, posted month by month Compound vs Simple Interestthe same deposit, two very different ledgers How Long to Double Your Moneydoubling time at every return, in one table Monthly Investment Calculatorno lump sum? the deposit-only ledger Compound Interest Calculatorthe main slip: deposits vs growth, posted

From the ledger

Why 72 works (and where it drifts)

Exact doubling solves (1 + r)^t = 2, giving t = ln 2 / ln(1 + r). The number 72 is a rounded stand-in for 100 × ln 2 ≈ 69.3, nudged up because it divides cleanly by 2, 3, 4, 6, 8, 9, and 12 — every return anyone quotes at a kitchen table. Between roughly 5% and 10% the shortcut lands within a few months of exact; at 2% it overstates slightly, at 15% it understates, and the slip’s side-by-side posting shows the drift instead of hiding it.

The rule cuts both ways, which the growth desk insists on posting: at 24% APR a credit-card balance doubles in about three years. Same 72, opposite sign. If the doubling line on your investments delights you, check the doubling line on your debts first.

Filed answers

Questions from the growth desk

How accurate is the Rule of 72?

Within about ±0.3 years between 5% and 10% returns. The slip posts the exact figure beside it so nothing rides on the shortcut.

What doubles at 4%?

About 18 years by the rule (72 ÷ 4), 17.4 exactly with monthly compounding. Savings-account growth is real, just slow.

Is this investment advice?

No — arithmetic on numbers you type.

Keep going

Also in the ledger

Savings Goal Calculatorworking backwards: what a goal needs each month Emergency Fund Calculatorfund the buffer first, then let growth run Debt Payoff Calculatorcompounding works against you here — clear it first Mortgage Calculatorthe same math, wearing a loan’s clothes Subscription Audit Calculatorfind the monthly deposit hiding in your subscriptions Hourly ↔ Salary Converterwhat the paycheck funding the deposit is worth