1. Foundation
Two formulas drive everything in this kit, and both are worth knowing exactly. The first is the future value of a lump sum: FV = PV × (1 + r)^n. PV is the present value (the amount you invest today), r is the periodic interest rate, and n is the number of periods. If you invest $10,000 at 7% per year for 30 years: FV = $10,000 × (1.07)^30 = $10,000 × 7.612 = $76,123. The second formula is the future value of a regular series of contributions (an annuity): FV = PMT × [(1 + r)^n − 1] / r. PMT is the payment per period, r is the rate per period, and n is the number of periods. If you contribute $500 per month for 30 years at 7% annual return (r = 7%/12 ≈ 0.5833% per month, n = 360 months): FV = $500 × [(1.005833)^360 − 1] / 0.005833 = $500 × [7.612 − 1] / 0.005833 = $500 × 1,133.5 = $566,765. These two formulas—lump sum and annuity—are the only math behind every projection in this kit.
The Rule of 72 is the fastest compound-interest shortcut you will use for the rest of your financial life. Divide 72 by the annual interest rate to find the approximate years it takes to double a sum of money. At 6%: 72/6 = 12 years to double. At 8%: 72/8 = 9 years. At 10%: 72/10 = 7.2 years. At 3% (a savings account or conservative bond): 72/3 = 24 years. At 12% (credit card debt): 72/12 = 6 years—meaning a credit card balance doubles every 6 years if you make no payments. The Rule of 72 also works in reverse: if you want your money to double in 10 years, you need a 7.2% return. This makes it instantly useful for evaluating whether a projected return is realistic, whether debt elimination should come before investing, and whether a financial product's promised yield is meaningful.
Lump-sum growth visualizer using FV = PV(1+r)^n across multiple rates and time horizons, showing the curve of compounding against a linear growth comparison. The visual makes the inflection point of compounding clear: growth is slow and nearly linear in the first decade, then accelerates sharply in the second and third decades. A $50,000 investment at 7% grows to $98,358 by year 10, $193,484 by year 20, and $380,613 by year 30. The amount earned in years 21 through 30 ($187,129) is nearly three times the amount earned in years 1 through 10 ($48,358), even though the time period is the same. That acceleration is why interrupting compounding—selling, withdrawing, switching accounts—in the middle decades destroys wealth disproportionately.
Regular contribution growth calculator using FV = PMT[(1+r)^n−1]/r that shows total contributions versus total interest earned, making the "time versus money" tradeoff explicit. At $300/month for 30 years at 7%, total contributions are $108,000 and total growth is $257,310 for a final balance of $365,310. The interest earned exceeds the money contributed by more than 2:1. At $300/month for only 20 years, total contributions are $72,000 and total growth is $82,286 for a balance of $154,286—the growth is less than the contributions. The decade between 20 and 30 years is where compounding shifts from underwhelming to extraordinary.
Age-22-versus-age-32 comparison tool that shows the cost of a 10-year delay in concrete dollars, using a standardized $300/month contribution at 7% annual return. Investor A starts at age 22 and contributes $300/month for 43 years until age 65. Investor B starts at age 32 and contributes $300/month for 33 years until age 65. Investor A's balance at 65: approximately $1,214,000. Investor B's balance at 65: approximately $572,000. Investor A ends up with $642,000 more despite contributing only $36,000 more in total ($3,600/year × 10 additional years). The extra $36,000 in contributions produced $606,000 in additional wealth through compounding. The 10-year head start is worth roughly 18 times its face value by age 65.