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Understand compound growth

Follow what happens when a percentage is applied repeatedly to a changing amount. Keep the calculation separate from any claim about an actual investment return.

Coins, a balance scale, and a clock illustrate quantities, tradeoffs, and time in financial learning.

What you’ll learn

  • Identify the balance used for each percentage calculation.
  • Explain how a compound calculation differs from repeating an unchanged amount.
  • State the assumptions behind a growth example.

The next calculation uses the new balance

With compounding, growth retained in the balance becomes part of the base for a later calculation. The percentage may stay the same while the amount it produces changes. This is a repeated percentage relationship, not the addition of the same fixed amount each time.

State the model before using it

A simple illustration may assume a fixed rate, one calculation per period, no withdrawals, and no additional costs. Write down those assumptions. Actual investment results can vary, include losses, and be affected by fees, taxes, and the timing of money moving in or out.

Common misunderstanding: the illustration predicts an investment

A neat upward sequence follows from the assumptions selected for the example. It does not establish that a real investment will grow at that rate or avoid losses. Use the model to understand the arithmetic and examine its conditions.

Worked example

Two periods at an illustrative 5%

Assume 1,000 grows by 5% at the end of each of two periods, with no other changes. After the first period it is 1,050. The next 5% is calculated on 1,050, adding 52.50 and producing 1,102.50. The second addition is larger because its base is larger. The rate is a teaching assumption, not a return forecast.

Learning paths that include this skill

Choose the route that fits your goal. The same skill can be useful in more than one subject or stage of learning.