Mental Math for Investing: Compound Growth, P/E, and Yield in Seconds
Investing runs on ratios, and most investors reach for a calculator when three or four mental identities would land the answer in under two seconds. Compound growth, price-earnings, dividend yield, and position sizing all collapse to shortcuts that fit in working memory. This piece is the working set. Seven identities, six anchor tables, and the drill order to lock each one.
Compound Growth Without a Spreadsheet
The Rule of 72 divides 72 by the annual rate to get doubling time in years. At 8 percent, money doubles in 9 years. At 12 percent, in 6. The Rule of 114 gives tripling time by dividing 114 by the rate, so 6 percent triples in 19 years. The Rule of 144 gives quadrupling time using the same shape. Swap 72 for 69.3 when rates run above 15 percent, since the approximation drifts past that band.
For a lump sum compounding at rate r over t years, the extra return above simple interest approximates r times t divided by 2, expressed as extra percent, for small products. A 5 percent bond over 10 years grows roughly 62 percent instead of the 50 percent a naive multiplication returns. For dollar-cost averaging, the effective compounding horizon on a monthly contribution runs about half the calendar span, so a 30-year plan behaves like a lump sum invested at year 15. That single adjustment fixes most retirement-target misestimates.
P/E Ratios and Earnings Yield in One Flip
Price-earnings ratio flips to earnings yield by dividing 100 by the P/E, the same percentage identity that turns tips into totals. A stock trading at 20x earns 5 percent, at 25x earns 4, at 10x earns 10. Compare that yield to the ten-year Treasury before you buy. Memorize six anchor pairs: 10 gives 10 percent, 12 gives 8.3, 15 gives 6.7, 20 gives 5, 25 gives 4, 30 gives 3.3.
Forward P/E flips the same way but uses next year's estimate instead of trailing earnings. PEG divides P/E by growth rate, and anything under 1 is cheap for the growth. Shiller PE runs on ten-year real earnings to smooth cycles, and the long-run average sits near 17, so a reading of 30 signals a rich market and 12 signals a cheap one.
Dividend Yield and Payout Coverage in Two Seconds
Dividend yield is annual dividend divided by share price. A $2 dividend on a $50 stock yields 4 percent. Divide the dividend by one percent of the price for a one-step read: $2 divided by $0.50 returns 4. Payout ratio is dividend divided by earnings per share, and a ratio above 80 percent flags a stretched payout that one bad quarter can force to cut.
Coverage ratio flips it: EPS divided by dividend. Under 1.25 is thin, over 2.0 is safe, above 3.0 is a growth candidate. Watch REITs and MLPs separately since they legally pay out most of income and report AFFO instead of EPS. A REIT payout ratio above 100 percent of net income can still be safe when AFFO covers it, because depreciation on real estate is a non-cash charge.
Position Sizing and Percentage Moves
Fixed-fraction sizing puts 1 to 2 percent of account equity at risk per trade, the same discipline that keeps poker bankrolls alive through variance. Risk equals entry price minus stop, times share count. Solve for share count as risk budget divided by per-share risk. A $50,000 account risking 1 percent has $500 to lose on any single position, so if the stop sits $2 below entry, size is 250 shares.
Percent gain and percent loss are not symmetric, and this asymmetry drives most compounding failures. A 20 percent loss requires a 25 percent gain to recover. A 50 percent loss requires 100 percent. A 75 percent loss requires 300 percent. Memorize the recovery table: 10 needs 11.1, 20 needs 25, 33 needs 50, 50 needs 100, 75 needs 300. The math answers the question every drawdown asks, which is how far back is even.
The Anchor Table Every Investor Should Memorize
Six number families cover roughly 80 percent of investing arithmetic. Load these into long-term memory before you load any single ticker, because a chart moves faster than a spreadsheet opens.
- Rule of 72 doubling times at whole rates from 3 to 15 percent, so 3 percent takes 24 years and 15 percent takes 4.8
- Earnings yield flips for P/E of 10, 12, 15, 20, 25, and 30
- Recovery gains needed for losses of 10, 20, 33, 50, and 75 percent
- Basis-point math: 100 bps equals 1 percent, 25 bps equals 0.25 percent, 50 bps equals half a percent
- CAGR shortcut: raise final over initial to the power of 1 divided by n, then subtract 1
- Fed-model spread: earnings yield minus the ten-year Treasury yield, positive means stocks look cheap against bonds
The Two-Week Drill
Days 1 through 4: recite the Rule of 72 doubling table at whole rates 3 through 15. Time each pass and aim for a sub-30-second full recall by day 4. Days 5 through 8: pick six random P/E numbers between 5 and 40 and flip each to earnings yield inside three seconds. Days 9 through 12: pull three real dividend stocks per day and compute yield plus coverage ratio without a calculator. Days 13 and 14: mix all three drills on a random-timer schedule, six problems per minute.
The pattern that works for pure arithmetic works here too: short bursts, honest scoring, and daily practice that compounds before it feels like it does. Once the anchors are loaded, run a Mathness session as a cooldown, because reactive target-number reps sharpen the same flip-and-anchor reflex the investing tables lean on. The reflex compounds like the returns.
