Saving/3 min exploration

When interest earns interest

Start with 100. Add nothing. Find the moment it doubles.

Experiment 0901 / YOUR INSTINCT

At a constant 5% annual interest rate, how many full years until 100 becomes at least 200?

This is a hypothetical account. Interest is added once at each year-end and stays in the account. There are no deposits, withdrawals, fees or taxes.

YOUR ESTIMATE

The dashed curve illustrates your guessed doubling year. It does not show the actual 5% growth yet.

Make your estimate10 years

1 year40 years

A rough guess is enough.

The bigger picture Hypothetical model · 5% annually

What the numbers mean

The rate stays the same. The amount it applies to grows.

After 14 years, the balance is about 197.99. After 15, it is about 207.89. Each year's interest joins the balance and earns interest itself, so the yearly additions gradually get bigger.

Read the sources

Watch the second year

In year one, 5% of 100 adds 5, leaving 105. In year two, 5% applies to 105, adding 5.25. That extra quarter is the first small sign of compounding. The Consumer Financial Protection Bureau uses the same annual process to explain why interest can grow on earlier interest. [1]

Time and the payment schedule both matter

With simple interest, the same 100 would earn 5 each year and reach 200 after 20 years. Our compound model reaches that threshold sooner because the base keeps growing. The SEC's calculator lets readers vary the rate, time, contributions and compounding frequency. Those inputs describe the scenario; changing them changes the result. [2]

A bigger balance can buy less than you expect

Doubling the number in an account does not guarantee twice the purchasing power. Inflation changes prices while the balance grows. The US Bureau of Labor Statistics explains how inflation adjustments separate money amounts from what they can buy. This edition keeps the rate fixed and leaves inflation out so the compounding mechanism is visible. [3]

Sources & method

How we worked it out.

Hypothetical model · 5% annually

Our model is 100 × 1.05^years, with interest credited only at whole year-ends. The first integer year with a balance of at least 200 is 15. Values are rounded only for display. The 5% rate is an assumption, not a forecast or product offer; actual rates, fees, taxes and inflation vary.