The Math That Rewards Starting Early

Simple interest pays you a percentage of your original deposit, every period, forever. Compound interest pays you a percentage of the current balance — original deposit plus every dollar of interest already earned. That second calculation is why a balance doesn't grow in a straight line; it curves upward, slowly at first, because each year's interest is calculated on a slightly larger number than the year before.

Put $1,000 in at 7% simple interest and you earn $70 every single year, always calculated on the original $1,000. After twenty years that's $1,000 plus twenty payments of $70, or $2,400 in total. Compound the same deposit at the same rate and year one still ends at $1,070 — but year two's interest is calculated on $1,070, not $1,000, so it pays $75 instead of $70. Carry that forward for twenty years and the compounded balance reaches $3,870 — $1,470 more than simple interest, from an identical rate and an identical deposit.

Over three years the gap is tiny — $1,225 compounded against $1,210 simple, $15 apart. That is the “rounding error” the lead paragraph mentioned, and it is exactly why compounding is easy to underestimate the first time you meet it. The gap doesn't look like anything until the years pile up.

There is a shortcut for turning any interest rate into “how long until this doubles,” accurate enough to use without a calculator: divide 72 by the rate. At 7%, 72 ÷ 7 is about 10.3 years. Work out the exact answer with the real compounding formula and it comes to 10.24 years — close enough that the shortcut earns its keep.

The shortcut is most accurate in the 6% to 10% range most long-term savers actually earn. It gets sloppier at very high or very low rates, but as a way to size up a rate in your head — a 401(k) match, a savings APY, a credit card APR — nothing beats it for speed.

The chart below runs two identical savers side by side: same monthly contribution, same 7% average annual return, same retirement age. The only difference is when they started. Adjust the slider and watch both totals move together — but never by the same amount.

Run the numbers once outside the chart, at its default setting. $200 a month at 7%, contributed for 40 years, becomes $524,963. The same $200 a month, at the same rate, contributed for only 30 years — starting ten years later and nothing else different — becomes $243,994. The difference is $280,968, which is larger than either saver's total contributions: $96,000 against $72,000. The extra $24,000 paid in over that decade explains a small slice of the gap. Compounding explains the rest.

This is the part that talks people out of starting. Early on, the balance looks almost exactly like the contributions — because at first, it is. Interest has barely had anything to work with yet.

1. 1

   Year 1 — balance $2,479

   Contributed $2,400. Growth so far: just $79.

2. 2

   Year 2 — balance $5,136

   Contributed $4,800. Growth so far: $336 — still small next to the deposits.

3. 3

   Year 5 — balance $14,319

   Contributed $12,000. Growth so far: $2,319.

4. 4

   Year 10 — balance $34,617

   Contributed $24,000. Growth so far: $10,617 — closing in, but contributions are still ahead.

5. 5

   Year 20 — balance $104,185

   Contributed $48,000. Growth so far: $56,185 — growth has now overtaken every dollar you put in.

6. 6

   Year 40 — balance $524,963

   Contributed $96,000. Growth: $428,963 — more than four dollars of growth for every dollar contributed.

It is tempting to chase a higher rate to make up for a late start. Time is doing more of the work than the rate is — a decade of extra compounding routinely outweighs a percentage point or two of extra return, and chasing yield usually means taking on more risk than the decade of patience would have cost you.

Put a number on it. Starting at 35 and reaching for 9% instead of 7% — $200 a month for 30 years — reaches $366,149. Starting at 25 at the ordinary 7% for 40 years still beats it, at $524,963. Two extra percentage points of return, which usually means meaningfully more risk, still loses to ten extra years of an unremarkable rate.

Compounding doesn't check whether the balance is helping you or hurting you — it applies exactly the same way to a debt left untouched. A $5,000 credit card balance at 24% APR, compounding monthly with no payments and no new charges, doesn't grow by $1,200 a year the way simple interest would suggest. It doubles. Run the rule of 72 the other direction: 72 ÷ 24 is 3. Left completely alone, that $5,000 becomes $10,000 in exactly three years — the identical mechanism that turned a decade of savings into an extra $280,968, now running against you.

No real card sits untouched for three years — minimum payments slow this down, which is the entire subject of the next two lessons in this track. But the direction of the maths doesn't change: a balance you don't pay down compounds exactly as reliably as a balance you do save into. It has no opinion about which one you meant.