How compounding frequency changes the result
Interest compounds when each period’s interest gets added to the balance and starts earning interest itself. The stated annual rate gets divided by the number of compounding periods per year, and that smaller rate applies that many times, so quarterly compounding applies a quarter of the annual rate four times, monthly applies a twelfth of it twelve times, and so on. More frequent compounding produces a slightly higher result at the same nominal annual rate, because interest starts compounding on itself sooner, but the effect is smaller than intuition suggests: the gap between annual and daily compounding at a typical rate is usually a few percent, not a dramatic difference.
Why compound growth accelerates over time
In the early years, most of the balance is still the original principal, and interest earned is a small addition. Given enough time, though, the accumulated interest itself becomes large enough to generate more new interest each year than the entire original principal generated in its first year. This is why compound growth charts look flat for a long stretch and then bend sharply upward: the underlying growth rate never changes, but the base it’s applied to keeps compounding on itself.
Reading the yearly table
Each row shows the account balance at the end of that year, calculated by applying the compounding formula for the exact number of periods elapsed. Because the rate is applied to a growing balance rather than a fixed principal, the dollar increase between consecutive years keeps growing even though the percentage rate never changes: that widening gap between rows is compound interest made visible.