Simple interest pays only on the original principal. For principal P, annual rate r as a decimal and time t in years:
FV_simple = P × (1 + r·t), where FV is future value.
Interest accrues in a straight line. ₹1,00,000 at 8% earns ₹8,000 every year, forever. You'll meet simple interest in short-term instruments and quotes, (many money-market conventions, penalty interest, coupon amounts between payment dates). You'll also meet it in any arrangement where the interest is paid out and not reinvested.
How does compound interest differ from simple interest?
Compound interest pays interest on interest. The balance itself becomes the base:
FV_compound = P × (1 + r)^t
Reinvestment does all the work. Watch ₹1,00,000 at 8%:
| Years | Simple: 1,00,000 × (1 + 0.08t) | Compound: 1,00,000 × 1.08^t | Compound − Simple |
|---|---|---|---|
| 1 | ₹1,08,000 | ₹1,08,000 | 0 |
| 5 | ₹1,40,000 | ₹1,46,933 | ₹6,933 |
| 10 | ₹1,80,000 | ₹2,15,892 | ₹35,892 |
| 20 | ₹2,60,000 | ₹4,66,096 | ₹2,06,096 |
| 30 | ₹3,40,000 | ₹10,06,266 | ₹6,66,266 |
| 40 | ₹4,20,000 | ₹21,72,452 | ₹17,52,452 |
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At year one they're identical. At year 40 compounding has produced five times the simple-interest outcome. The line is straight, and the curve bends away from it forever. Every "the first decade looks unimpressive" story about wealth is this table. So is every "how did that company get so big" story about businesses reinvesting profits at high returns. A company that earns 20% on its capital and reinvests it is running (1.20)^t on your behalf, and that's the reason Phase 2 will teach you to measure ROIC so carefully.
Think in doublings. The most useful mental unit for compound growth is the double. Doubling takes 1 to 2 to 4 to 8, so three doublings make 8×. If you know how long one doubling takes, you can size decades in your head. At 12%, one doubling takes about 6 years, so 18 years ≈ 8×. At 6%, a doubling takes about 12 years, so the same 18 years ≈ 2.8×. Count in doublings and the percentages take care of themselves.
Where does the Rule of 72 come from?
How long does money take to double at rate r? Working it out gives you the Rule of 72 as a by-product. If logarithms make you wince, stay with it, because it's only two lines. Solve for t:
(1 + r)^t = 2
Take logarithms of both sides. A logarithm just asks "what exponent produced this number?", and ln is the natural log, the log with base e ≈ 2.71828.
t × ln(1 + r) = ln 2, so t = ln 2 / ln(1 + r), and ln 2 = 0.6931…
That's exact. Now for the approximation that turns it into mental arithmetic. For small r, ln(1 + r) ≈ r. Check it yourself: ln(1.08) = 0.0770, close to 0.08. Substitute:
t ≈ 0.693 / r = 69.3 / (r in %)
So the derivation actually gives you a "Rule of 69.3." Why does everyone use 72? There are two reasons. First, ln(1+r) is always slightly smaller than r, so dividing by r understates the true doubling time. A slightly bigger numerator corrects the bias in the range of rates people actually meet. At 8%, the exact answer is 9.01 years. 69.3/8 = 8.66 is noticeably short, while 72/8 = 9.00 is nearly perfect. Second, 72 divides beautifully: by 2, 3, 4, 6, 8, 9, 12. Far from folklore, the rule is a calibrated instrument:
| Rate | Exact doubling time (ln 2 / ln(1+r)) | Rule of 72 | Verdict |
|---|---|---|---|
| 2% | 35.0 yrs | 36.0 | close |
| 4% | 17.7 | 18.0 | close |
| 6% | 11.9 | 12.0 | excellent |
| 8% | 9.01 | 9.00 | essentially exact |
| 10% | 7.27 | 7.20 | excellent |
| 12% | 6.12 | 6.00 | good |
| 15% | 4.96 | 4.80 | fair |
| 24% | 3.22 | 3.00 | rule now undershoots |
| 36% | 2.25 | 2.00 | rule breaks down |
When does the Rule of 72 work, and what are the companion rules?
Use it between roughly 4% and 15%, and outside that band compute exactly. Run the same derivation with ln 3 and ln 4 and you get two companion rules, the Rule of 114 for tripling (114/r) and the Rule of 144 for quadrupling, which is two doublings. It also runs on anything growing steadily. At ~7% real GDP growth an economy doubles in ~10 years. At 6% inflation the price level doubles in ~12 years, so the purchasing power of an unlucky rupee halves every 12 years. The Rule of 72 is an inflation ruler as well.