Simple & Compound Interest

Put 10000 in a bank and the bank pays you a little thank-you every year: interest. How is it calculated? Two rules exist, and after 30 years the gap between them will make you sit up straight.

Simple interest: the same slice every year

Simple interest is computed on the original deposit only. Call the principal P (the money you start with), the yearly rate r, and the time t in years. The interest is:

$I = P \times r \times t$

With 10000 at 5% per year, each year earns $10000 \times 0.05 = 500$ , year after year — 1500 after three years. Year 1 pays 500, year 10 still pays 500. Draw the total and you get a straight line, exactly the $y = mx + b$ shape from Equation of a Straight Line.

Compound interest: the interest starts earning too

Compound interest changes one rule, and that changes everything: each year the interest joins the principal, and the next year it earns interest too. After t years the total is:

$A = P \times (1 + r)^t$

Same 10000 at 5%: after year one it is 10500; year two is computed on 10500, giving $10500 \times 1.05 = 11025$ ... the money starts rolling like a snowball. Working with letter formulas is old news if you met Variables & the Function Machine.

InteractiveCompound Curve

How to use

Principal10000Annual rate 5%5Years10

Simple

15,000

Compound

16,289

Compound earns extra: +1,289

Try it: the first two years

10000 at 5% for two years. Simple: $10000 + 500 \times 2 = 11000$ . Compound: $10000 \times 1.05^2 = 11025$ . Only 25 apart? Do not dismiss it — those 25 are the interest earned by the first 500 of interest. Every snowball starts small.

The Rule of 72: years to double

A mental-math gem: divide 72 by the yearly rate (drop the percent sign) and you get roughly the number of years it takes to double.

At 8%: $72 \div 8 = 9$ years to double;
At 6%: about 12 years;
At 3%: about 24 years.

It is an approximation, most accurate between 4% and 12%. For a quick verdict on whether money is growing fast enough, it is all you need.

Why starting early wins

Same 10000, same 5%, left to compound:

Left 10 years: about 16289, a gain of 6289;
Left 30 years: about 43219, a gain of 33219.

Under simple interest those 30 years would yield $10000 + 500 \times 30 = 25000$ — about 18000 less than compound. The late game is where compound shines: the first decade earns 6289, the last decade about 16686 — more than double. Time feeds the snowball, which is why every early year counts.

Compound interest cuts both ways

When you save, it works for you; when you owe, it works for the bank. Credit card debt often runs near 20% a year — by the Rule of 72 it doubles in about 3.6 years. In debt, compound interest sits on the other side of the table.

Check yourself

Quick quiz

0 / 3 correct0 / 3 correct

1. 10000 sits at simple interest, 5% a year. How much interest after 3 years?
2. By the Rule of 72, how long does money take to double at 8%?
3. Same 10000 at the same 5%. After 30 years, how do simple and compound compare?