What is compound interest?

Compound interest is interest that is calculated on the original principal plus all the interest added in earlier periods. Because each period's interest becomes part of the base for the next, the balance grows by a rising amount each time rather than a fixed one. It matters for decisions because small differences in rate or time horizon produce very large differences in the final balance, for savers and borrowers alike.

How it works

The core feedback loop is simple: the balance produces interest, and the interest is added to the balance. With principal P, a rate r per period and n periods, the balance is P × (1 + r)^n. Simple interest, by contrast, grows only by P × r each period, which is a straight line, while compounding bends upward into an exponential curve. The same loop works against you on debt: unpaid interest is added to what you owe, and the next charge is larger.

Two levers matter most. The first is the rate per period, and how often it is applied, since monthly compounding adds interest to the base more often than yearly compounding at the same stated rate. The second is time, because the curve is flat early and steep late, so the final years contribute most of the growth.

Example

Say you deposit 1,000 at 5% per year with no withdrawals. After one year the balance is 1,050. In year two, interest is 5% of 1,050, which is 52.50, so the balance becomes 1,102.50. With simple interest the balance would be 1,100, so the extra 2.50 is interest on interest. After 20 years, compounding gives 1,000 × 1.05^20, about 2,653, while simple interest gives only 2,000. The gap keeps widening each year. This is an illustration with round numbers, not a forecast of any real account.

How to model it in Machinations

Use a Pool for the balance and a Source connected to it that adds resources each step. Make the Source's rate a Register that multiplies the Pool's current value by the interest rate, linked with a state connection from the Pool to the Register. Expose the rate as a Lever. Play for 20 steps and chart the Pool, then change the rate or add a Drain for withdrawals to see how quickly the curve flattens.