Interest and compounding

Compounding is the most boring superpower in finance. It is also the closest thing to magic the math allows. If you understand it deeply, almost every other decision about money becomes easier.

Simple interest first

Simple interest is interest paid only on your original deposit. Put $1,000 in an account that pays 5% simple interest per year. Each year you earn $50, no matter how long you leave it. After 10 years you have $1,500. After 30 years you have $2,500. The growth is linear.

Almost nothing in the real world works this way. Simple interest is mostly a teaching example. The interesting stuff happens with compound interest.

Compound interest changes the game

Compound interest is interest paid on your original deposit AND on all the interest you have already earned. Each year, the base your interest is calculated on is bigger than the year before. The growth curves upward.

Same $1,000, same 5% rate, but compounded annually: after one year you have $1,050. The next year you earn 5% on $1,050, not $1,000, so you end with $1,102.50. The third year you earn on $1,102.50. After 10 years you have $1,629. After 30 years, $4,322. After 50 years, $11,467.

Compare that to simple interest: simple gives you $3,500 after 50 years. Compound gives you $11,467. Same rate, same starting amount, three times the result. The only difference is whether the interest itself earns interest.

The Rule of 72

There is a quick mental shortcut for compound interest called the Rule of 72. To estimate how many years it takes for an investment to double, divide 72 by the annual interest rate.

• At 2% annual return: 72 / 2 = 36 years to double.
• At 6% annual return: 72 / 6 = 12 years to double.
• At 10% annual return: 72 / 10 = roughly 7 years to double.
• At 24% credit card debt: 72 / 24 = your debt doubles in 3 years if you do not pay it.

It is not exact, but it is close enough to be useful. Memorize it. It will save you a calculator a hundred times.

Why starting late hurts so much

Imagine two siblings. Anna invests $5,000 a year from age 25 to 35, then stops contributing entirely. Total invested: $50,000 over ten years. Ben starts at 35 and invests $5,000 a year until he is 65. Total invested: $150,000 over thirty years.

At an 8% annual return (assuming each $5,000 is invested at the start of the year), by age 65 Anna has roughly $787,000. Ben has about $612,000. Anna invested a third as much money and ended up with more, simply because her early dollars had decades longer to compound.

This is why every financial guide screams about starting young. It is not motivational fluff. The math is genuinely brutal in the other direction. Every decade you delay investing roughly halves what your eventual nest egg could have been.

Compounding works against you too

The same force that builds wealth on investments destroys wealth on debt. Credit card APRs of 22 to 28 percent are absolutely vicious because the interest is being charged on a balance that grows every month you do not pay it off.

A $5,000 credit card balance at 24% APR, paying only the minimum, takes over 20 years to clear and costs you more than $13,000 in interest. The credit card company is using compounding against you, and it is the same math that would have built your portfolio if you had invested instead.

Compound interest is the eighth wonder of the world. He who understands it, earns it. He who doesn't, pays it.

Often attributed to Albert Einstein