Question

How does the saying "money breeds money" apply to simple interest?

Answer 1

"Money breeds money" fits simple interest, but only in a limited, linear way.

Simple interest formula:
A = P(1 + r t),
where P = principal, r = annual interest rate (decimal), t = years.
Interest earned after t years is I = P r t. That means each dollar of principal generates a fixed amount of interest per year (Pr per year). So more principal -> more interest, i.e. money produces more money.

Key points:
- The interest earned each period is constant: every year you get Pr, not interest on the interest. Interest does not "breed" additional interest.
- Growth is linear, not exponential. Doubling time under simple interest is t = 1/r (at 5% simple interest you need 20 years to double), whereas compound interest doubles much faster (roughly 72/r years with the rule of 72 for moderate r).
- Simple interest is a good model for short-term loans or instruments where interest isn’t reinvested; for long-term growth, compound interest better captures the idea that money’s offspring can themselves produce more offspring.

So the proverb is true under simple interest — money does make money — but it won’t produce accelerating growth unless the interest is allowed to compound.