Interest is a slice

Savings interest of 5% a year means each year the bar grows by a slice that is 5% of how long it already is.

Start with $1,000. After a year the slice is $50, so the bar is $1,050. Next year the slice is 5% of $1,050, which is $52.50, so the bar is $1,102.50.

The slice grows because the bar it is cut from grows. That is all compounding is: this year's bar is last year's bar plus a slice of itself.

One question

You save $1,000 at 5% a year, added once a year. How much is there after two years?

Say it backIn your own words: why is the second year's interest bigger than the first?

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