Examples · Money · updated 2026-09-26

Does 5% a year for 10 years mean a 50% increase?

No. A starting amount of 100 growing at 5% a year, compounded for 10 years, reaches about 162.89. Each year's 5% applies to the balance at that point, not to the original 100. Change the years on the board below and check.

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On the left are the starting amount, the annual rate and the years. The right-hand column is, from the top, Simple growth, the difference and Compound growth. Simple growth adds "5% of the original 100" every year; compound growth applies 5% to the balance each year. The difference sits between them.

5% times 10 years: 50%?

The quick answer is 5% × 10 = 50%, so 100 → 150.

That adds 5% of the original 100 every year — 5 a year, every year. The board's Simple growth shows 150 too.

With compound growth, next year starts from a bigger number

With compound growth, each year's result becomes the starting point for the next.

Year 1 — 100 × 1.05 = 105
Year 2 — 105 × 1.05 = 110.25
Year 3 — 110.25 × 1.05 = 115.7625

Repeat that 10 times and you have 100 × 1.05¹⁰. After 10 years that is 162.889463, about 162.89.

The rate is 5% every year, but the number it applies to gets bigger every year.

The left card on the board below does exactly this, one year at a time. Set the count to 1, 2 and 3 and you get 105, 110.25 and 115.7625; set it to 10 and you get 162.889463, the same as the compound growth on the board above.

Open in CalcAnyway ↗

You can change the numbers here too, but changes made in this frame are not saved. To keep them, open it in CalcAnyway and edit there.

Where does the gap between 150 and 162.89 come from?

Simple growth gives 150, compound growth about 162.89: a difference of about 12.89.

With simple growth, the yearly increase stays at 5 for ever. With compound growth, the 5 added in year 1 also earns 5% in year 2. What has already been added earns the next 5% too. That keeps stacking up, and after 10 years it comes to about 12.89.

Try it yourself

Keep the annual rate at 5% and set the years to 1, 5, 10, 20 and 30.

Starting amount 100, annual rate 5% (measured on the board, rounded to 2 decimal places)
Years	Simple growth	Compound growth	Difference
1	105	105	0
5	125	about 127.63	about 2.63
10	150	about 162.89	about 12.89
20	200	about 265.33	about 65.33
30	250	about 432.19	about 182.19

After one year they are the same. The longer it runs, the faster the gap grows, because growth-on-growth keeps repeating for every extra year.

How long does 5% growth take to double?

The right-hand card on the second board, Doubling time, works out how many periods it takes to double at 5% a period. Here one period is one year: about 14.21 years.

With simple growth, reaching 200 takes 20 years (see the table). Compound growth gets there about six years sooner.

The card also shows the rule of 72: 72 ÷ 5 = 14.4 years, a rough estimate that comes close to the exact 14.21.

Read next — If something falls 20% and then rises 20%, is it back where it started? The same idea: one percentage, applied to different starting values, gives different amounts.

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