Compound Interest & the Time Value of Money

Tier 0 · Foundations · beginner · ~3 min read · compoundingsavinginvestingtime-value-of-money

The one idea to take from this page

If you remember nothing else about money, remember this: interest earns interest.

When you put money somewhere that pays a return — a savings account, an index fund, a bond — you earn interest on what you put in. The twist is that next year you also earn interest on last year’s interest. That second layer is small at first and then, quietly, it becomes the whole story. This is compound interest, and it is the engine underneath almost everything else in finance.

The flip side has a name too: a dollar today is worth more than a dollar next year, because today’s dollar can start earning right now. That is the time value of money — the same idea, viewed from the other end.

See it for yourself

The chart below shows a balance growing over time. The blue area is the money you actually put in. The teal area on top is interest — money the money made for you. Drag the sliders and watch the teal overtake the blue.

Things worth trying

• Slide Years from 10 to 40. Notice the balance doesn’t just grow — it bends upward. Doubling the time far more than doubles the result. That curve is compounding.
• Set Monthly contribution to 0 and raise Starting amount. A lump sum left alone still grows. Time does the work even when you stop adding.
• Compare a long horizon at a modest rate against a short horizon at a high rate. Time usually wins. This is why “start early” beats “pick the perfect investment”.

Why the curve bends

Straight-line growth would mean adding the same amount every year. Compounding adds a percentage every year, and the percentage applies to an ever-larger balance. Early on, the balance is small, so the interest is small and the line looks almost straight. Later, the balance is large, the interest on it is large, and the line steepens. The longer you let it run, the more dramatic the bend — which is why the last decade of a long horizon often adds more than the first three combined.

The rule of 72

A quick mental shortcut: divide 72 by your annual return to estimate how many years it takes your money to double.

• At 6%, money doubles in about 12 years (72 ÷ 6).
• At 9%, about 8 years (72 ÷ 9).

It’s an approximation, but it’s close enough to reason about in your head — and it makes the cost of a couple of extra percentage points obvious.

What this means in practice

1. Time is your biggest lever. Starting earlier beats saving more later, often by a lot. The simulator makes this visceral — try it.
2. Small, regular contributions compound. You don’t need a windfall. Consistency over a long horizon does the heavy lifting.
3. The same math runs in reverse on debt. Carry a balance on a high-interest loan and compounding works against you just as hard. (That’s the next tier.)

Key terms

• Principal — the money you start with or put in.
• Rate of return — the annual percentage your money grows.
• Compounding period — how often interest is added back (here, monthly).
• Time value of money — a dollar now is worth more than a dollar later, because it can start earning today.

Next up in Foundations: budgeting and cash flow — how to free up the money you’ll feed into this curve.